Relevant papers for my research

We compute in detail the absorption optical depth for astrophysical γ-ray photons interacting with solar photons to produce electron positron pairs. This effect is greatest for γ-ray sources at small angular distances from the Sun, reaching optical depths as high as \tau_γγ∼10^-2. We also calculate this effect including modifications to the absorption cross section threshold from subluminal Lorentz invariance violation (LIV). We show for the first time that subluminal LIV can lead to increases or decreases in \tau_γγ compared to the non-LIV case. We show that, at least in principle, LIV can be probed with this effect with observations of γ-ray sources near the Sun at \gtrsim20 TeV by HAWC or LHAASO, although a measurement will be extremely difficult due to the small size of the effect.

A hypothetical photon mass, m_γ, can produce a frequency-dependent vacuum dispersion of light, which leads to an additional time delay between photons with different frequencies when they propagate through a fixed distance. The dispersion measure–redshift measurements of fast radio bursts (FRBs) have been widely used to constrain the rest mass of the photon. However, all current studies analyzed the effect of the frequency-dependent dispersion for massive photons in the standard \LambdaCDM cosmological context. In order to alleviate the circularity problem induced by the presumption of a specific cosmological model based on the fundamental postulate of the masslessness of photons, here we employ a new model-independent smoothing technique, Artificial Neural Network (ANN), to reconstruct the Hubble parameter H(z) function from 34 cosmic- chronometer measurements. By combining observations of 32 well-localized FRBs and the H(z) function reconstructed by ANN, we obtain an upper limit of m_γ \le 3.5 \times 10^-51;\rmkg, or equivalently m_γ \le 2.0 \times 10^-15;\rmeV/c^2 (m_γ \le 6.5 \times 10^-51;\rmkg, or equivalently m_γ \le 3.6 \times 10^-15;\rmeV/c^2) at the 1σ(2σ) confidence level. This is the first cosmology-independent photon mass limit derived from extragalactic sources.

The Lorentz Invariance Violation (LIV), a proposed consequence of certain quantum gravity (QG) scenarios, could instigate an energy-dependent group velocity for ultra-relativistic particles. This energy dependence, although suppressed by the massive QG energy scale E_\mathrmQG, expected to be on the level of the Planck energy 1.22 \times 10^19 GeV, is potentially detectable in astrophysical observations. In this scenario, the cosmological distances traversed by photons act as an amplifier for this effect. By leveraging the observation of a remarkable flare from the blazar Mrk 421, recorded at energies above 100 GeV by the MAGIC telescopes on the night of April 25 to 26, 2014, we look for time delays scaling linearly and quadratically with the photon energies. Using for the first time in LIV studies a binned-likelihood approach we set constraints on the QG energy scale. For the linear scenario, we set 95% lower limits E_\mathrmQG>2.7\times10^17 GeV for the subluminal case and E_\mathrmQG> 3.6 \times10^17 GeV for the superluminal case. For the quadratic scenario, the 95% lower limits for the subluminal and superluminal cases are E_\mathrmQG>2.6 \times10^10 GeV and E_\mathrmQG>2.5\times10^10 GeV, respectively.

In this paper, the acceleration of particles in astrophysical sources by the Fermi mechanism is revisited under the assumption of Lorentz invariance violation (LIV). We calculate the energy spectrum and the acceleration time of particles leaving the source as a function of the energy beyond which the Lorentz invariance violation becomes relevant. Lorentz invariance violation causes significant changes in the acceleration of particles by the first and second-order Fermi mechanisms. The energy spectrum of particles accelerated by first-order Fermi mechanism under LIV assumption shows a strong suppression for energies above the break. The calculations presented here complete the scenario for LIV searches with astroparticles by showing, for the first time, how the benchmark acceleration mechanisms (Fermi) are modified under LIV assumption.

Time-of-flight measurements of high-energy astrophysical neutrinos can be used to probe Lorentz invariance, a pillar of modern physics. If Lorentz-invariance violation (LIV) occurs, it could cause neutrinos to slow down, with the delay scaling linearly or quadratically with their energy. We introduce non-parametric statistical methods designed to detect LIV-induced distortions in the temporal structure of a high-energy neutrino flare as it travels to Earth from a distant astrophysical source, independently of the intrinsic timing properties of the source. Our approach, illustrated using the 2014/2015 TeV-PeV neutrino flare from the blazar TXS 0506+056 detected by IceCube, finds that the LIV energy scale must exceed 10^14 GeV (linear) or 10^9 GeV (quadratic). Our methods provide a robust means to investigate LIV by focusing solely on a neutrino flare, without relying on electromagnetic counterparts, and account for realistic energy and directional uncertainties. For completeness, we compare our limits inferred from TXS 0506+056 to the sensitivity inferred from multi- messenger detection of tentative coincidences between neutrinos and electromagnetic emission from active galactic nuclei and tidal disruption events.

Lorentz invariance violation (LIV) in gamma rays can have multiple consequences, such as energy-dependent photon group velocity, photon instability, vacuum birefringence, and modified electromagnetic interaction. Depending on how LIV is introduced, several of these effects can occur simultaneously. Nevertheless, in experimental tests of LIV, each effect is tested separately and independently. For the first time, we are attempting to test for two effects in a single analysis: modified gamma-ray absorption and energy-dependent photon group velocity. In doing so, we are using artificial neural networks. In this contribution, we discuss our experiences with using machine learning for this purpose and present our very first results.

In the gravity quantum theory, the quantization of spacetime may lead to the modification of the dispersion relation between the energy and the momentum and the Lorentz invariance violation (LIV). High energy and long-distance gamma-ray bursts (GRBs) observations in the universe provide a unique opportunity to test the possibility of LIV. In this paper, by using 93 time delay GRBs covering the redshift range of 0.117 < z < 6.29, we present a new idea of using cosmological model-independent (based on the luminosity distance data from 174 GRBs) to test the LIV. Combining the observation data from multiband of GRBs provides us with an opportunity to mitigate the potential systematic errors arising from variations in the physical characteristics among diverse object populations, and to add a higher redshift dataset for testing the energy- dependent velocity caused by the corrected dispersion relationship of photons. These robust limits of the energy scale for the linear and quadratic LIV effects are E_QG,1 \ge 1.40\times 10^15 GeV, and E_QG,2 \ge 8.18\times 10^9 GeV, respectively. It exhibits a significantly reduced value compared to the energy scale of Planck in both scenarios of linear and quadratic LIV.

We reanalyze the spectral lag data for 56 Gamma-Ray Bursts (GRBs) in the cosmological rest frame to search for Lorentz Invariance Violation (LIV) using frequentist inference. For this purpose, we use the technique of profile likelihood to deal with the nuisance parameters, corresponding to a constant time lag in the GRB rest frame and an unknown intrinsic scatter, while the parameter of interest is the energy scale for LIV (E_QG). With this method, we do not obtain a global minimum for χ^2 as a function of E_QG up to the Planck scale. Thus, we can obtain one-sided lower limits on E_QG in a seamless manner. Therefore, the 95% c.l. lower limits which we thus obtain on E_QG are then given by: E_QG≥2.07 \times 10^14 GeV and E_QG≥3.71\times 10^5 GeV, for linear and quadratic LIV, respectively.

Lorentz invariance is the cornerstone of relativity theory. Its implications have been verified experimentally with a variety of approaches. The detection of a muon at extremely high energy detected by the ARCA detector in the Mediterranean sea, the most energetic particle directly measured up to date, allows to put additional constraints on Lorentz non-invariant theories. The prediction of some of those theories is that the lifetimes of particles in the laboratory frame ’decrease’ rather than ’increase’ with increasing γ. In this frame the sheer fact that the muon traversed the whole ARCA detector puts a lower limit on the muon lifetime in the laboratory frame, that implies upper limits on Lorentz violating parameters.

Lorentz symmetry is a cornerstone of both the General relativity and Standard Model and its experimental verification deepens our understanding of nature. This paper focuses on the investigation of Lorentz violations with the context of clock comparison experiments in the framework of Standard Model Extension (SME). Considering matter-gravity coupling sector, we provide a generic frame to study the sensitivities of Lorentz-violating coefficients for three distinct types of clock redshift tests, including the traditional gravitational redshift test, null-redshift test I and null-redshift test II. Each of these tests is sensitivity to different combinations of Lorentz-violating coefficients. By using the current clock comparison results, we estimate the limits of SME coefficients at level of parts in 10^4 down to parts in 10^7. Better sensitivity may be achieved in the clock comparisons by using the state-of-the- art optical clocks. Additionally considering relativistic factors in null- redshift I, the frequency comparison result of E2 and E3 transitions of Yb^+ can set the limit c^e_00=(7.4\pm9.3)\times10^-9 in the electron sector. Our analysis demonstrates that clock-comparison redshift experiments may contribute to explore the vast parameters space on searching for the Lorentz violation.

One of the manifestations of Lorentz invariance violation (LIV) is vacuum birefringence, which leads to an energy-dependent rotation of the polarization plane of linearly polarized photons arising from an astrophysical source. Here we use the energy-resolved polarization measurements in the prompt γ-ray emission of five bright gamma-ray bursts (GRBs) to constrain this vacuum birefringent effect. Our results show that at the 95% confidence level, the birefringent parameter ηcharacterizing the broken degree of Lorentz invariance can be constrained to be |η|<\mathcalO(10^-15-10^-16), which represent an improvement of at least eight orders of magnitude over existing limits from multi-band optical polarization observations. Moreover, our constraints are competitive with previous best bounds from the single γ-ray polarimetry of other GRBs. We emphasize that, thanks to the adoption of the energy-resolved polarimetric data set, our results on ηare statistically more robust. Future polarization measurements of GRBs at higher energies and larger distances would further improve LIV limits through the birefringent effect.

Lorentz invariance violation (LV) is examined through the time delay between high-energy and low-energy photons in gamma-ray bursts (GRBs). Previous studies determined the LV energy scale as E_\rm LV ≃3.60 \times 10^17 GeV using Fermi Gamma-ray Space Telescope (FGST) data. This study updates the time- delay model and reaffirms these findings with new observations. High-energy photons from GRBs at GeV and TeV bands are analyzed, including the 99.3 GeV photon from GRB 221009A (FGST), the 1.07 TeV photon from GRB 190114C (MAGIC), and the 12.2 TeV photon from GRB 221009A (LHAASO). Our analysis, in conjunction with previous data, consistently shows that high-energy photons are emitted earlier than low-energy photons at the source. By evaluating 17 high-energy photons from 10 GRBs observed by FGST, MAGIC, and LHAASO, we estimate the LV energy scale to be E_\rm LV ≃3.00 \times 10^17 GeV. The null hypothesis of dispersion-free vacuum E=pc (or, equivalently, the constant light-speed v_γ=c) is rejected at a significance level of 3.1σor higher.

Lorentz invariance violation (LIV) has long been recognized as an observable low-energy signature of quantum gravity. In spite of a great effort to detect LIV effects, so far only lower bounds have been derived. The high energy photons from the gamma ray burst GRB 221009A have been detected by the LHAASO collaboration and one at \cal E ≃251  \rm TeV by the Carpet collaboration using a partial data set. Very recently, the Carpet collaboration has completed the full data analysis, reporting further support for their previously detected photon now at \cal E = 300^+ 43_- 38  \rm TeV, which manifestly clashes with conventional physics. Taking this result at face value, we derive the first evidence for LIV and we show that such a detection cannot be explained by axion-like particles (ALPs), which allow for the observation of the highest energy photons detected by LHAASO. We also outline a scenario in which ALPs and LIV naturally coexist. If confirmed by future observations our finding would represent the first positive result in quantum gravity phenomenology.

Several observational phenomena suggest that the standard model of cosmology and particle physics requires revision. To address this, we consider the extension of general relativity known as massive gravity (MG). In this Letter, we explore the imprints of MG on the propagation of gravitational waves (GWs): their modified dispersion relation and their additional (two vector and one scalar) polarization modes on the stochastic GW background (SGWB) detected by pulsar timing arrays (PTAs). We analyze the effects of massive GWs on the Hellings- Downs curve induced by modification of the overlap reduction function. Our study consists of analyzing observational data from the NANOGrav 15-year dataset and the Chinese PTA Data Release I, and is independent of the origin of the SGWB (astrophysical or cosmological). By considering the bound on the graviton mass imposed through the dispersion relation, we scrutinize the possibility of detecting traces of MG in the PTA observational data. We find that massive GWs predict better fits for the observed pulsar correlations. Future PTA missions with more precise data will hopefully be able to detect the GW additional polarization modes and might be effectively used to constrain the graviton mass.

Convincing evidence of a stochastic gravitational wave (GW) background has been found by the NANOGrav Collaboration in the 15-year data set. From this signal, we can evaluate the possibility of its source being from the early Universe through the tensor perturbations induced by a massive spin-2 graviton field. We consider a time-dependent model of the minimal theory of massive gravity and find values of the graviton mass, mass cutoff time, and Hubble rate of inflation that amplify the energy spectra of primordial GWs sufficiently to reproduce the signal from the NANOGrav data within 1-3 standard deviation. However, a suppression mechanism for high-frequency modes must be introduced to conservatively obey the big bang nucleosynthesis (BBN) bound. While there are regions of the parameter space that reproduce the signal, it remains a challenge to simultaneously respect the BBN and cosmic microwave background bounds without making the graviton mass cutoff time too deep into the matter-dominated era.

Dimensional flow, the scale dependence of the dimensionality of spacetime, is a feature shared by many theories of quantum gravity (QG). We present the first study of the consequences of QG dimensional flow for the luminosity distance scaling of gravitational waves in the frequency ranges of LIGO and LISA. We find generic modifications with respect to the standard general-relativistic scaling, largely independent of specific QG proposals. We constrain these effects using two examples of multimessenger standard sirens, the binary neutron-star merger GW170817 and a simulated supermassive black-hole merger event detectable with LISA. We apply these constraints to various QG candidates, finding that the quantum geometries of group field theory, spin foams and loop quantum gravity can give rise to observable signals in the gravitational-wave spin-2 sector. Our results complement and improve GW propagation-speed bounds on modified dispersion relations. Under more model-dependent assumptions, we also show that bounds on quantum geometry can be strengthened by solar-system tests.

Inflation with Weyl scaling symmetry provides a viable scenario that can generate both the nearly scaling invariant primordial density fluctuation and a dark matter candidate. Here we point out that, in additional to the primordial gravitational waves (GWs) from quantum fluctuations, the production of high- frequency GWs from preheating in such inflation models can provide an another probe of the inflationary dynamics. We conduct both linear analytical analysis and nonlinear numerical lattice simulation in a typical model. We find that significant stochastic GWs can be produced and the frequency band is located around 10^8 Hz ∼10^9 Hz, which might be probed by future resonance- cavity experiments.

Gravitational waves induced by large primordial curvature fluctuations may result in a sizable stochastic gravitational wave background. Interestingly, curvature fluctuations are gradually generated by initial isocurvature fluctuations, which in turn induce gravitational waves. Initial isocurvature fluctuations commonly appear in multi-field models of inflation as well as in the formation of scattered compact objects in the very early universe, such as primordial black holes and solitons like oscillons and cosmic strings. Here we provide a review on isocurvature induced gravitational waves and its applications to dark matter and the primordial black hole dominated early universe.

In this paper, we analyze parity-violating effects in the propagation of gravitational waves (GWs). For this purpose, we adopt a newly proposed parametrized post-Einstenian (PPE) formalism, which encodes modified gravity corrections to the phase and amplitude of GW waveforms. In particular, we focus our study on three well-known examples of parity-violating theories, namely Chern-Simons, Symmetric Teleparallel and Horǎva-Lishitz gravity. For each model, we identify the PPE parameters emerging from the inclusion of parity- violating terms in the gravitational Lagrangian. Thus, we use the simulated sensitivities of third-generation GW interferometers, such as the Einstein Telescope and Cosmic Explorer, to obtain numerical bounds on the PPE coefficients and the physical parameters of binary systems. In so doing, we find that deviations from General Relativity cannot be excluded within given confidence limits. Moreover, our results show an improvement of one order of magnitude in the relative accuracy of the GW parameters compared to the values inferred from the LIGO-Virgo-KAGRA network. In this respect, the present work demonstrates the power of next-generation GW detectors to probe fundamental physics with unprecedented precision.

Chain inflation is an alternative to slow-roll inflation in which the inflaton tunnels along a large number of consecutive minima in its potential. In this work we perform the first comprehensive calculation of the gravitational wave spectrum of chain inflation. In contrast to slow-roll inflation the latter does not stem from quantum fluctuations of the gravitational field during inflation, but rather from the bubble collisions during the first-order phase transitions associated with vacuum tunneling. Our calculation is performed within an effective theory of chain inflation which builds on an expansion of the tunneling rate capturing most of the available model space. The effective theory can be seen as chain inflation’s analogue of the slow-roll expansion in rolling models of inflation. We show that chain inflation produces a very characteristic double-peak spectrum: a faint high-frequency peak associated with the gravitational radiation emitted during inflation, and a strong low-frequency peak associated with the graceful exit from chain inflation (marking the transition to the radiation-dominated epoch). There exist very exciting prospects to test the gravitational wave signal from chain inflation at the aLIGO-aVIRGO-KAGRA network, at LISA and /or at pulsar timing array experiments. A particularly intriguing possibility we point out is that chain inflation could be the source of the stochastic gravitational wave background recently detected by NANOGrav, PPTA, EPTA and CPTA. We also show that the gravitational wave signal of chain inflation is often accompanied by running/ higher running of the scalar spectral index to be tested at future Cosmic Microwave Background experiments.

We consider the effects of backreaction on axion-SU(2) dynamics during inflation. We use the linear evolution equations for the gauge field modes and compute their backreaction on the background quantities numerically using the Hartree approximation. We show that the spectator chromo-natural inflation attractor is unstable when back-reaction becomes important. Working within the constraints of the linear mode equations, we find a new dynamical attractor solution for the axion field and the vacuum expectation value of the gauge field, where the latter has an opposite sign with respect to the chromo-natural inflation solution. Our findings are of particular interest to the phenomenology of axion-SU(2) inflation, as they demonstrate the instability of the usual trajectory due to large backreaction effects. The viable parameter space of the model becomes significantly altered, provided future non-Abelian lattice simulations confirm the existence of the new dynamical attractor. In addition, the backreaction effects lead to characteristic oscillatory features in the primordial gravitational wave background that are potentially detectable with upcoming gravitational wave detectors.

The angular correlation of pulsar residuals observed by NANOGrav and other pulsar timing array (PTA) collaborations show evidence in support of the Hellings-Downs correlation expected from stochastic gravitational wave background (SGWB). In this paper, we offer a non-gravitational wave explanation of the observed pulsar timing correlations as caused by an ultra-light L_μ - L_τ gauge boson dark matter (ULDM). ULDM can affect the pulsar correlations in two ways. The gravitational potential of vector ULDM gives rise to a Shapiro time delay of the pulsar signals and a non-trivial angular correlation (as compared to the scalar ULDM case). In addition, if the pulsars have a non-zero charge of the dark matter gauge group, then the electric field of the local dark matter causes an oscillation of the pulsar and a corresponding Doppler shift of the pulsar signal. We point out that pulsars carry a significant charge of muons, and thus the L_μ - L_τ vector dark matter contributes to both the Doppler oscillations and the time delay of the pulsar signals. The synergy between these two effects provides a better fit to the shape of the angular correlation function, as observed by the NANOGrav collaboration, compared to the standard SGWB explanation or the SGWB combined with time delay explanations. Our analysis shows that in addition to the SGWB signal, there may potentially be excess timing residuals attributable to the L_μ - L_τ ULDM.

Scalar induced gravitational waves contribute to the cosmological gravitational wave background. They can be related to the primordial density power spectrum produced towards the end of inflation and therefore are a convenient new tool to constrain models of inflation. These waves are sourced by terms quadratic in perturbations and hence appear at second order in cosmological perturbation theory. While the focus of research so far was on purely scalar source terms we also study the effect of including first order tensor perturbations as an additional source. This gives rise to two additional source terms: a term quadratic in the tensor perturbations and a cross term involving mixed scalar and tensor perturbations. We present full analytical expressions for the spectral density of these new source terms and discuss their general behaviour. To illustrate the generation mechanism we study two toy models containing a peak on small scales. For these models we show that the scalar-tensor contribution becomes non-negligible compared to the scalar-scalar contribution on smaller scales. We also consider implications for future gravitational wave surveys.

We compute the stochastic gravitational wave (GW) background generated by black hole-black hole (BH-BH) hyperbolic encounters with eccentricities close to one and compare them with the respective sensitivity curves of planned GW detectors. We use the Keplerian potential to model the orbits of the encounters and the quadrupole formula to compute the emitted GWs. We take into account hyperbolic encounters that take place in clusters up to redshift 5 and with BH masses spanning from 5 M_⊙ to 55 M_⊙. We assume the clusters to be virialized and study several cluster models with different mass and virial velocity, and finally obtain an accumulative result, displaying the background as an average. Using the maxima and minima of our accumulative result for each frequency, we provide analytical expressions for both optimistic and pessimistic scenarios. Our results suggest that the background from these encounters is likely to be detected by the third-generation detectors Cosmic explorer and Einstein telescope, while the tail section at lower frequencies intersects with DECIGO, making it a potential target source for both ground- and space-based future GW detectors.

We investigate the stochastic gravitational waves background arising from the first-order QCD chiral phase transition, considering three distinct sources: bubble collisions, sound waves, and fluid turbulence. Within the framework of the Polyakov-Nambu-Jona-Lasinio (PNJL) model, we calculate the parameters governing the intensity of the gravitational wave phase transition and determine their magnitudes along the adiabatic evolutionary path. We introduce the effective bag constant B_\mathrmeff related to the dynamical evolution of quarks to evaluate the intensity of the phase transition. By calculating expanded potential at the point of false vacuum, we find that all the bubbles are in the mode of runaway, leading the velocity of the bubble wall to the speed of light. The resulting gravitational wave energy spectrum is estimated, revealing a characteristic amplitude of the generated gravitational waves within the centihertz frequency range. We present the gravitational wave spectrum and compare it with the sensitivity range of detectors, and find that the gravitational wave spectra generated by these sources have the potential to be detected by future detectors such as BBO and \muARES.

We study the possibility of using the LiteBIRD satellite B-mode survey to constrain models of inflation producing specific features in CMB angular power spectra. We explore a particular model example, i.e. spectator axion-SU(2) gauge field inflation. This model can source parity-violating gravitational waves from the amplification of gauge field fluctuations driven by a pseudoscalar "axionlike" field, rolling for a few e-folds during inflation. The sourced gravitational waves can exceed the vacuum contribution at reionization bump scales by about an order of magnitude and can be comparable to the vacuum contribution at recombination bump scales. We argue that a satellite mission with full sky coverage and access to the reionization bump scales is necessary to understand the origin of the primordial gravitational wave signal and distinguish among two production mechanisms: quantum vacuum fluctuations of spacetime and matter sources during inflation. We present the expected constraints on model parameters from LiteBIRD satellite simulations, which complement and expand previous studies in the literature. We find that LiteBIRD will be able to exclude with high significance standard single-field slow-roll models, such as the Starobinsky model, if the true model is the axion- SU(2) model with a feature at CMB scales. We further investigate the possibility of using the parity-violating signature of the model, such as the TB and EB angular power spectra, to disentangle it from the standard single-field slow- roll scenario. We find that most of the discriminating power of LiteBIRD will reside in BB angular power spectra rather than in TB and EB correlations.

Recent observations from several pulsar timing array (PTA) collaborations have unveiled compelling evidence for a stochastic signal in the nanohertz band. This signal aligns remarkably with a gravitational wave (GW) background, potentially originating from the first-order color charge confinement phase transition. Distinct quantum chromodynamics (QCD) matters, such as quarks or gluons, and diverse phase transition processes thereof can yield disparate GW energy density spectra. In this paper, employing the Bayesian analysis on the NANOGrav 15-year data set, we explore the compatibility with the observed PTA signal of the GW from phase transitions of various QCD matter scenarios in the framework of the holographic QCD. We find that the PTA signal can be effectively explained by the GW from the confinement-deconfinement phase transition of pure quark systems in a hard wall model of the holographic QCD where the bubble dynamics, one important source of the GWs, is of the Jouguet detonations. Notably, our analysis decisively rules out the plausibility of the pure gluon QCD-matter scenario and the non-runaway bubble dynamics model for the phase transition in explaining the observed PTA signal.

Astrometry, the precise measurement of star motions, offers an alternative avenue to investigate low-frequency gravitational waves through the spatial deflection of photons, complementing pulsar timing arrays reliant on timing residuals. Upcoming data from Gaia and Roman can not only cross-check pulsar timing array findings but also explore the uncharted frequency range bridging pulsar timing arrays and LISA. We present an analytical framework to evaluate the feasibility of detecting a gravitational wave background, considering measurement noise and the intrinsic variability of the stochastic background. Furthermore, we highlight astrometry’s crucial role in uncovering key properties of the gravitational wave background, such as spectral index and chirality, employing information-matrix analysis. Finally, we simulate the emergence of quadrupolar correlations, commonly referred to as the generalized Hellings-Downs curves.

The recent compelling observation of the nanohertz stochastic gravitational wave background has brought to light a new galactic arena to test gravity. In this paper, we derive a formula for the most general expression of the stochastic gravitational wave background correlation that could be tested with pulsar timing and future square kilometer arrays. Our expressions extends the harmonic space analysis, also often referred to as the power spectrum approach, to predict the correlation signatures of an anisotropic polarized stochastic gravitational wave background with subluminal tensor, vector, and scalar gravitational degrees of freedom. We present the first few nontrivial anisotropy and polarization signatures in the correlation and discuss their dependence on the gravitational wave speed and pulsar distances. Our results set up tests that could potentially be used to rigorously examine the isotropy of the stochastic gravitational wave background and strengthen the existing constraints on possible non-Einsteinian polarizations in the nanohertz gravitational wave regime.

We explore the capability of measuring lensing signals in LiteBIRD full-sky polarization maps. With a 30 arcmin beam width and an impressively low polarization noise of 2.16\,\muK-arcmin, LiteBIRD will be able to measure the full-sky polarization of the cosmic microwave background (CMB) very precisely. This unique sensitivity also enables the reconstruction of a nearly full-sky lensing map using only polarization data, even considering its limited capability to capture small-scale CMB anisotropies. In this paper, we investigate the ability to construct a full-sky lensing measurement in the presence of Galactic foregrounds, finding that several possible biases from Galactic foregrounds should be negligible after component separation by harmonic-space internal linear combination. We find that the signal-to-noise ratio of the lensing is approximately 40 using only polarization data measured over 90% of the sky. This achievement is comparable to Planck’s recent lensing measurement with both temperature and polarization and represents a four-fold improvement over Planck’s polarization-only lensing measurement. The LiteBIRD lensing map will complement the Planck lensing map and provide several opportunities for cross-correlation science, especially in the northern hemisphere.

We perform a phenomenological comparison of the gravitational wave (GW) spectrum expected from cosmic gauge string networks and superstring networks comprised of multiple string types. We show how violations of scaling behavior and the evolution of the number of relativistic degrees of freedom in the early Universe affect the GW spectrum. We derive simple analytical expressions for the GW spectrum from superstrings and gauge strings that are valid for all frequencies relevant to pulsar timing arrays (PTAs) and laser interferometers. We analyze the latest data from PTAs and show that superstring networks are consistent with 32 nHz data from NANOGrav, but are excluded by 3.2 nHz data at 3σunless the string coupling g_s<0.2 or the strings evolve in only about 10% of the volume of the higher-dimensional space. We also point out that while gauge string networks are excluded by NANOGrav-15 data at 3σ, they are completely compatible with EPTA and PPTA data. Finally, we study correlations between GW signals at PTAs and laser interferometers.

Early matter-dominated eras (EMDEs) are a natural feature arising in many models of the early universe and can generate a stochastic gravitational wave background (SGWB) during the transition from an EMDE to the radiation-dominated universe required by the time of Big Bang Nucleosynthesis. While there are calculations of the SGWB generated in the linear regime, no detailed study has been made of the nonlinear regime. We perform the first comprehensive calculation of GW production in the nonlinear regime, using a hybrid N-body and lattice simulation to study GW production from both a metastable matter species and the radiation produced in its decay. We find that nonlinearities significantly enhance GW production up to frequencies at least as large as the inverse light-crossing time of the largest halos that form prior to reheating. The resulting SGWB is within future observational reach for curvature perturbations as small as those probed in the cosmic microwave background, depending on the reheating temperature. Out-of-equilibrium dynamics could further boost the induced SGWB, while a fully relativistic gravitational treatment is required to resolve the spectrum at even higher frequencies.

Parity violation in the gravitational sector is a prediction of many theories beyond general relativity. In the propagation of gravitational waves, parity violation manifests by inducing amplitude and/or velocity birefringence between right- and left-circularly polarized modes. We study how the stochastic gravitational wave background can be used to place constraints on these birefringent effects. We consider two model scenarios, one in which we allow birefringent corrections to become arbitrarily large, and a second in which we impose stringent theory priors. In the former, we place constraints on a generic birefringent gravitational-wave signal due to the current non-detection of a stochastic background from compact binary events. We find a joint constraint on birefringent parameters, \kappa_D and \kappa_z, of \mathcalO(10^-1). In the latter scenario, we forecast constraints on parity violating theories resulting from observations of the future upgraded LIGO-Virgo-KAGRA network as well as proposed third-generation detectors. We find that third-generation detectors will be able to improve the constraints by at least two orders of magnitude, yielding new stringent bounds on parity violating theories. This work introduces a novel and powerful probe of gravitational parity violation with gravitational-wave data.

We discuss the present state and planned updates of CosmoLattice, a cutting-edge code for lattice simulations of non-linear dynamics of scalar-gauge field theories in an expanding background. We first review current capabilities of the code, including the simulation of interacting singlet scalars and of Abelian and non-Abelian scalar-gauge theories. We also comment on new features recently implemented, such as the simulation of gravitational waves from scalar and gauge fields. Secondly, we discuss new extensions of CosmoLattice that we plan to release publicly. On the one hand, we comment on new physics modules, which include axion-gauge interactions φF \widetildeF, non-minimal gravitational couplings φ^2 R, creation and evolution of cosmic defect networks, and magneto-hydro-dynamics (MHD). On the other hand, we discuss new technical features, including evolvers for non-canonical interactions, arbitrary initial conditions, simulations in 2+1 dimensions, and higher accuracy spatial derivatives.

In this paper, we review the theoretical basis for generation of gravitational waves and the detection techniques used to detect a gravitational wave. To materialize this goal in a thorough way we first start with a mathematical background for general relativity from which a clue for gravitational wave was conceived by Einstein. Thereafter we give the classification scheme of gravitational waves such as (i) continuous gravitational waves, (ii) compact binary inspiral gravitational waves and (iii) stochastic gravitational wave. Necessary mathematical insight into gravitational waves from binaries are also dealt with which follows detection of gravitational waves based on the frequency classification. Ground based observatories as well as space borne gravitational wave detectors are discussed in a length. We have provided an overview on the inflationary gravitational waves. In connection to data analysis by matched filtering there are a few highlights on the techniques, e.g. (i) Random noise, (ii) power spectrum, (iii) shot noise, and (iv) Gaussian noise. Optimal detection statistics for a gravitational wave detection is also in the pipeline of the discussion along with detailed necessity of the matched filter and deep learning.

We discuss the gravitational wave (GW) spectra predicted from the electroweak scalegenesis of the Higgs portal type with a large number of dark chiral flavors, which many flavor QCD would underlie and give the dynamical explanation of the negative Higgs portal coupling required to trigger the electroweak symmetry breaking. We employ the linear-sigma model as the low-energy description of dark many flavor QCD and show that the model undergoes ultra- supercooling due to the produced strong first-order thermal phase transition along the (approximately realized) flat direction based on the Gildener-Weinberg mechanism. Passing through evaluation of the bubble nucleation/percolation, we address the reheating and relaxation processes, which are generically non- thermal and nonadiabatic. Parametrizing the reheating epoch in terms of the e-folding number, we propose proper formulae for the redshift effects on the GW frequencies and signal spectra. It then turns out that the ultra-supercooling predicted from the Higgs-portal scalegenesis generically yields none of GW signals with the frequencies as low as nano Hz, unless the released latent heat is transported into another sector other than reheating the universe. Instead, models of this class prefer to give the higher frequency signals and still keeps the future prospected detection sensitivity, like at LISA, BBO, and DECIGO, etc. We also find that with large flavors in the dark sector, the GW signals are made further smaller and the peak frequencies higher. Characteristic phenomenological consequences related to the multiple chiral scalars include the prediction of dark pions with the mass much less than TeV scale, which is also briefly addressed.

One of the major challenges in particle physics and cosmology is understanding why there is an asymmetry between matter and antimatter in the Universe. One possible explanation for this phenomenon is thermal leptogenesis, which involves the addition of at least two right-handed neutrinos (RHNs) to the standard model. Another possible explanation is baryogenesis through the hypermagnetic fields which involves the \rm U_Y(1) anomaly and helical hypermagnetic fields in the early Universe. In this paper, after reviewing the thermal leptogenesis and baryogenesis through the \rm U_Y(1) anomaly, we investigate the simplest model that combines these two scenarios and explore the parameter space for optimal results. Our results show that the combined scenario permits a specific region of parameter space that is not covered by either one separately. In fact, the minimum required mass scale of the RHN and strength of initial hypermagnetic helicity are reduced by one order of magnitude in our model. Moreover, we find that in the combined scenario, leptogenesis and baryogenesis through the \rm U_Y(1) anomaly can either amplify or reduce the effect of each other, i.e., the generated asymmetry, depending on the sign of the helical hypermagnetic fields. Finally, we show the surprising result that a drastic amplification can occur even when the initial abundance of RHN is its equilibrium value for leptogenesis.

By leveraging the limits on primordial magnetic fields (PMFs), their contributions to secondary gravitational waves (GWs), and the recent observations by the pulsar timing arrays (PTAs), we arrive at constraints on the epoch of reheating. We find that the combined spectral energy density of primary and secondary (generated by the PMFs) GWs can be described as a broken power law with different indices. We show that PMFs with blue spectra and appropriate reheating scenarios can successfully explain the PTA observations without invoking any new physics.

For most of cosmic history, the evolution of our Universe has been governed by the physics of a ’dark sector’, consisting of dark matter and dark energy, whose properties are only understood in a schematic way. The influence of these constituents is mediated exclusively by the force of gravity, meaning that insight into their nature must be gleaned from gravitational phenomena. The advent of gravitational-wave astronomy has revolutionised the field of black hole astrophysics, and opens a new window of discovery for cosmological sources. Relevant examples include topological defects, such as domain walls or cosmic strings, which are remnants of a phase transition. Here we present the first simulations of cosmic structure formation in which the dynamics of the dark sector introduces domain walls as a source of stochastic gravitational waves in the late Universe. We study in detail how the spectrum of gravitational waves is affected by the properties of the model, and extrapolate the results to scales relevant to the recent evidence for a stochastic gravitational wave background. Our relativistic implementation of the field dynamics paves the way for optimal use of the next generation of gravitational experiments to unravel the dark sector.

Gravitational waves are a unique probe of the early Universe, as the Universe is transparent to gravitational radiation right back to the end of inflation. In this article, we summarise detection prospects and the wide scope of primordial events that could lead to a detectable stochastic gravitational wave background. Any such background would shed light on what lies beyond the Standard Model, sometimes at remarkably high scales. We overview the range of strategies for detecting a stochastic gravitational wave background before delving deep into three major primordial events that can source such a background. Finally, we summarize the landscape of other sources of primordial backgrounds.

Gravitational wave astronomy has emerged as a new branch of observational astronomy, since the first detection of gravitational waves in 2015. The current number of O(100) detections is expected to grow by several orders of magnitude over the next two decades. As a result, current computationally expensive detection algorithms will become impractical. A solution to this problem, which has been explored in the last years, is the application of machine-learning techniques to accelerate the detection and parameter estimation of gravitational wave sources. In this chapter, several different applications are summarized, including the application of artificial neural networks and autoenconders in accelerating the computation of surrogate models, deep residual networks in achieving rapid detections with high sensitivity, as well as artificial neural networks for accelerating the construction of neutron star models in an alternative theory of gravity.

The Hellings and Downs correlation curve describes the correlation of the timing residuals from pairs of pulsars as a function of their angular separation on the sky and is a smoking-gun signature for the detection of an isotropic stochastic background of gravitational waves. We show that it can be easily obtained from realizing that Lorentz transformations are conformal transformations on the celestial sphere and from the conformal properties of the two-point correlation of the timing residuals. This result allows several generalizations, e.g. the calculation of the three-point correlator of the time residuals and the inclusion of additional polarization modes (vector and/or scalar) arising in alternative theories of gravity.

The NANOGrav, Parkes and European Pulsar Timing Array (PTA) experiments have collected strong evidence for a stochastic gravitational wave background in the nHz-frequency band. In this work we perform a detailed statistical analysis of the signal in order to elucidate its physical origin. Specifically, we test the standard explanation in terms of supermassive black hole mergers against the prominent alternative explanation in terms of a first-order phase transition. By means of a frequentist hypothesis test we find that the observed gravitational wave spectrum prefers a first-order phase transition at 2-3σsignificance compared to black hole mergers (depending on the underlying black hole model). This mild preference is linked to the relatively large amplitude of the observed gravitational wave signal (above the typical expectation of black hole models) and to its spectral shape (which slightly favors the phase-transition spectrum over the predominantly single power-law spectrum predicted in black hole models). The best fit to the combined PTA data set is obtained for a phase transition which dominantly produces the gravitational wave signal by bubble collisions (rather than by sound waves). The best-fit (energy-density) spectrum features, within the frequency band of the PTA experiments, a crossover from a steeply rising power law (causality tail) to a softly rising power law; the peak frequency then falls slightly above the PTA-measured range. Such a spectrum can be obtained for a strong first-order phase transition in the thick-wall regime of vacuum tunneling which reheats the Universe to a temperature of T_*∼\textGeV. A dark sector phase transition at the GeV-scale provides a comparably good fit.

Advancements in cosmology through next-generation ground-based gravitational wave observatories will bring in a paradigm shift. We explore the pivotal role that gravitational-wave standard sirens will play in inferring cosmological parameters with next-generation observatories, not only achieving exquisite precision but also opening up unprecedented redshifts. We examine the merits and the systematic biases involved in gravitational-wave standard sirens utilizing binary black holes, binary neutron stars, and neutron star-black hole mergers. Further, we estimate the precision of bright sirens, golden dark sirens, and spectral sirens for these binary coalescences and compare the abilities of various next-generation observatories (A^sharp, Cosmic Explorer, Einstein Telescope, and their possible networks). When combining different sirens, we find sub-percent precision over more than 10 billion years of cosmic evolution for the Hubble expansion rate H(z). This work presents a broad view of opportunities to precisely measure the cosmic expansion rate, decipher the elusive dark energy and dark matter, and potentially discover new physics in the uncharted Universe with next-generation gravitational-wave detectors.

Slow first-order phase transitions generate large inhomogeneities that can lead to the formation of primordial black holes (PBHs). We show that the gravitational wave (GW) spectrum then consists of a primary component sourced by bubble collisions and a secondary one induced by large perturbations. The latter gives the dominant peak if β/H_0 < 12, impacting, in particular, the interpretation of the recent PTA data. The GW signal associated with a particular PBH population is stronger than in typical scenarios because of a negative non-Gaussianity of the perturbations and it has a distinguishable shape with two peaks.

"If one could ever prove the existence of gravitational waves, the processes responsible for their generation would probably be much more curious and interesting than even the waves themselves." (Gustav Mie, 1868 - 1957) The discovery of gravitational waves has opened new windows on astrophysics, cosmology and physics beyond the Standard Model (BSM). Measurements by the LIGO, Virgo and KAGRA Collaborations of stellar-mass binaries and neutron star mergers have shown that gravitational waves travel at close to the velocity of light, and also constrain BSM possibilities such as a graviton mass and Lorentz violation in gravitational wave propagation. Follow-up measurements of neutron star mergers have provided evidence for the production of heavy elements, possibly including some essential for human life. The gravitational waves in the nanoHz range observed by Pulsar Timing Arrays (PTAs) may have been emitted by supermassive black hole binaries, but might also have originated from BSM cosmological scenarios such as cosmic strings, or phase transitions in the early Universe. The answer to the question in the title may be provided by gravitational-wave detectors at higher frequencies, such as LISA and atom interferometers.

We study gravitational wave production during kinetic preheating after inflation with a focus on scenarios that arise in α-attractor models where a scalar dilaton-like inflaton is kinetically coupled to a second scalar field. We present high-resolution lattice simulations of three α-attractor models for a range of parameters to probe regions where preheating is efficient. We find that preheating in these models can be extremely violent, resulting in gravitational wave energy densities that can be constrained by cosmic microwave background measurements of the effective number of relativistic species, N_\rm eff

Understanding the nature of primordial fluctuations is pivotal to unraveling the Universe’s early evolution. While these fluctuations are observed to be nearly scale-invariant, quasi-adiabatic, and Gaussian on large scales, their small- scale behavior remains poorly constrained, offering a potential window into new physics. Recent detections of a stochastic gravitational wave background in the nanohertz frequency range by pulsar timing arrays (PTAs), including NANOGrav, PPTA, EPTA+InPTA, and CPTA, align with astrophysical predictions from supermassive black hole binaries but could also encode signatures of primordial phenomena. We investigate whether the observed signal originates from primordial isocurvature or adiabatic fluctuations by fitting them to the latest NANOGrav dataset. Through comprehensive Bayesian model comparison, we evaluate the distinguishability of these scenarios given current PTA sensitivities. Our results demonstrate that existing data cannot conclusively differentiate between isocurvature and adiabatic sources, highlighting the need for enhanced observational capabilities to probe the primordial universe at small scales.

Recent Pulsar Timing Array (PTA) collaborations show strong evidence for a stochastic gravitational wave background (SGWB) with the characteristic Hellings-Downs inter-pulsar correlations. The signal may stem from supermassive black hole binary mergers, or early universe phenomena. The former is expected to be strongly anisotropic while primordial backgrounds are likely to be predominantly isotropic with small fluctuations. In case the observed SGWB is of cosmological origin, our relative motion with respect to the SGWB rest frame is a guaranteed source of anisotropy, leading to \textitO(10^-3) energy density fluctuations of the SGWB. For such cosmological SGWB, kinematic anisotropies are likely to be larger than the intrinsic anisotropies, akin to the cosmic microwave background (CMB) dipole anisotropy. We assess the sensitivity of current PTA data to the kinematic dipole anisotropy, and we also forecast at what extent the magnitude and direction of the kinematic dipole can be measured in the future with an SKA-like experiment. We also discuss how the spectral shape of the SGWB and the location of the pulsars to monitor affect the prospects of detecting the kinematic dipole with PTA. In the future, a detection of this anisotropy may even help resolve the discrepancy in the magnitude of the kinematic dipole as measured by CMB and large-scale structure observations.

The scalar and tensor fluctuations generated during inflation can be correlated, if arising from the same underlying mechanism. In this paper we investigate such correlation in the model of axion inflation, where the rolling inflaton produces quanta of a U(1) gauge field which, in turn, source scalar and tensor fluctuations. We compute the primordial correlator of the curvature perturbation, ζ, with the gravitational energy density, \Omega_GW, at frequencies probed by gravitational wave detectors. This two-point function receives two contributions: one arising from the correlation of gravitational waves with the scalar perturbations generated by the standard mechanism of amplification of vacuum fluctuations, and the other coming from the correlation of gravitational waves with the scalar perturbations sourced by the gauge field. Our analysis shows that the former effect is generally dominant. For typical values of the parameters, the correlator, normalized by the amplitude of ζand by the fractional energy in gravitational waves at interferometer frequencies, turns out to be of the order of 10^-4\div 10^-2.

We develop a tool for the analysis of stochastic gravitational wave backgrounds from cosmological first-order phase transitions with LISA: we initiate a template databank for these signals, prototype their searches, and forecast their reconstruction. The templates encompass the gravitational wave signals sourced by bubble collisions, sound waves and turbulence. Accounting for Galactic and extra-Galactic foregrounds, we forecast the region of the parameter space that LISA will reconstruct with better than ∼10\,% accuracy, if certain experimental and theoretical uncertainties are solved by the time LISA flies. We illustrate the accuracy with which LISA can reconstruct the parameters on a few benchmark signals, both in terms of the template parameters and the phase transition ones. To show the impact of the forecasts on physics beyond the Standard Model, we map the reconstructed benchmark measurements into the parameter spaces of the singlet extension of the Standard Model and of the classically conformal invariant U(1)_B-L model.

There is solid theoretical and observational motivation behind the idea of scale-invariance as a fundamental symmetry of Nature. We consider a recently proposed classically scale-invariant inflationary model, quadratic in curvature and featuring a scalar field non-minimally coupled to gravity. We go beyond earlier analytical studies, which showed that the model predicts inflationary observables in qualitative agreement with data, by solving the full two-field dynamics of the system – this allows us to corroborate previous analytical findings and set robust constraints on the model’s parameters using the latest Cosmic Microwave Background (CMB) data from Planck and BICEP/Keck. We demonstrate that scale-invariance constrains the two-field trajectory such that the effective dynamics are that of a single field, resulting in vanishing entropy perturbations and protecting the model from destabilization effects. We derive tight upper limits on the non-minimal coupling strength, excluding conformal coupling at high significance. By explicitly sampling over them, we demonstrate an overall insensitivity to initial conditions. We argue that the model \textitpredicts a minimal level of primordial tensor modes set by r ≳0.003, well within the reach of next-generation CMB experiments. These will therefore provide a litmus test of scale-invariant inflation, and we comment on the possibility of distinguishing the model from Starobinsky and α-attractor inflation. Overall, we argue that scale-invariant inflation is in excellent health, and possesses features which make it an interesting benchmark for tests of inflation from future CMB data.

We explore the possibility of producing the observed matter-antimatter asymmetry of the Universe uniquely from the evaporation of primordial black holes (PBH) that are formed in an inflaton-dominated background. Considering the inflaton (φ) to oscillate in a monomial potential V(φ)∝φ^n, we show, it is possible to obtain the desired baryon asymmetry via vanilla leptogenesis from evaporating PBHs of initial mass ≲10 g. We find that the allowed parameter space is heavily dependent on the shape of the inflaton potential during reheating (determined by the exponent of the potential n), the energy density of PBHs (determined by β), and the nature of the coupling between the inflaton and the Standard Model (SM). To complete the minimal gravitational framework, we also include in our analysis the gravitational leptogenesis set-up through inflaton scattering via exchange of graviton, which opens up an even larger window for PBH mass, depending on the background equation of state. We finally illustrate that such gravitational leptogenesis scenarios can be tested with upcoming gravitational wave (GW) detectors, courtesy of the blue-tilted primordial GW with inflationary origin, thus paving a way to probe a PBH-induced reheating together with leptogenesis.

We forecast high-frequency gravitational wave (GW) from preheating hosting gravitational dark matter (GDM) as the indirect probe of such GDM. We use proper lattice simulations to handle resonance, and to solve GW equation of motion with the resonance induced scalar field excitations as source term. Our numerical results show that Higgs scalar excitations in Higgs preheating model give rise to magnitudes of GW energy density spectra of order 10^-10 at frequencies 10-10^3 MHz depending on the GDM mass, whereas inflaton fluctuation excitations in inflaton self-resonant preheating model yield magnitudes of GW energy density spectrum up to 10^-9 (10^-11) at frequencies near 30 (2) MHz for the index n=4 (6) with respect to the GDM mass of 1.04 (2.66)\times 10^14 GeV.

In this work we study the power spectrum of the Stochastic Gravitational Wave Background produced by standard and biased domain wall networks, using the Velocity-dependent One-Scale model to compute the cosmological evolution of their characteristic scale and root-mean-squared velocity. We consider a standard radiation + Λ\rm CDM background and assume that a constant fraction of the energy of collapsing domain walls is emitted in the form of gravitational waves. We show that, in an expanding background, the total energy density in gravitational radiation decreases with cosmic time (after a short initial period of quick growth). We also propose a two parameter model for the scale-dependence of the frequency distribution of the gravitational waves emitted by collapsing domain walls. We determine the corresponding power spectrum of the Stochastic Gravitational Wave Background generated by domain walls, showing that it is a monotonic decreasing function of the frequency for frequencies larger than that of the peak generated by the walls that have decayed most recently. We also develop an analytical approximation to this spectrum, assuming perfect linear scaling during both the radiation and matter eras, in order to characterize the dependence of the amplitude, peak frequency and slope of the power spectrum on the model parameters.

We argue that the axionic domain-wall with a QCD bias may be incompatible with the NANOGrav 15-year data on a stochastic gravitational wave (GW) background, when the domain wall network collapses in the hot-QCD induced local CP-odd domain. This is due to the drastic suppression of the QCD bias set by the QCD topological susceptibility in the presence of the CP-odd domain with nonzero θparameter of order one which the QCD sphaleron could generate. We quantify the effect on the GW signals by working on a low-energy effective model of Nambu-Jona-Lasinio type in the mean field approximation. We find that only at θ=\pi, the QCD bias tends to get significantly large enough due to the criticality of the thermal CP restoration, which would, however, give too big signal strengths to be consistent with the NANOGrav 15-year data and would also be subject to the strength of the phase transition at the criticality.

The vast majority of gravitational-wave signals from stellar-mass compact binary mergers are too weak to be individually detected with present-day instruments and instead contribute to a faint, persistent background. This astrophysical background is targeted by searches that model the gravitational-wave ensemble collectively with a small set of parameters. The traditional search models the background as a stochastic field and estimates its amplitude by cross- correlating data from multiple interferometers. A different search uses gravitational-wave templates to marginalize over all individual event parameters and measure the duty cycle and population properties of binary mergers. Both searches ultimately estimate the total merger rate of compact binaries and are expected to yield a detection in the coming years. Given the conceptual and methodological differences between them, though, it is not well understood how their results should be mutually interpreted. In this paper, we use the Fisher information to study the implications of a background detection in terms of which region of the Universe each approach probes. Specifically, we quantify how information about the compact binary merger rate is accumulated by each search as a function of the event redshift. For the LIGO Design sensitivity and a uniform-in-comoving-volume distribution of equal-mass 30M_sol binaries, the traditional cross-correlation search obtains 99% of its information from binaries up to redshift 2.5 (average signal-to-noise-ratio <8), and the template-based search from binaries up to redshift 1.0 (average signal-to-noise- ratio  8). While we do not calculate the total information accumulated by each search, our analysis emphasizes the need to pair any claimed detection of the stochastic background with an assessment of which binaries contribute to said detection.

If an early matter phase of the Universe existed after inflation with the proper power spectrum, enhanced density perturbations can decouple from the Hubble flow, turn around and collapse. In contrast to what happens in a radiation dominated Universe where pressure nullifies deviations from sphericity in these perturbations, in a matter dominated Universe, the lack of pressure although on the one hand facilitates the gravitational collapse, it allows small deviations from sphericity to grow substantially as the collapse takes place. The subsequent collapse is complicated: initially as non-spherical deviations grow, the collapsing cloud takes the form of a “Zel’dovich pancake". After that, the more chaotic and nonlinear stage of violent relaxation begins where shells of the cloud cross and the matter is redistributed within a factor of a few of the free fall timescale, reaching a spherical virialized state. During the whole process, strong gravitational waves are emitted due to the anisotropy of the collapse and the small time interval that the effect takes place. The emission of gravitational waves during the stage of the violent relaxation cannot be easily estimated with an analytical model. We perform an N-body simulation to capture the behaviour of matter during this stage in order to estimate the precise spectrum of gravitational waves produced in this scenario.

Over the last few years, primordial black holes (PBHs) have emerged as a strong candidate for cold dark matter. A significant number of PBHs are produced when the strength of the primordial scalar power spectrum is enhanced on small scales (compared to the COBE normalized values on large scales). Such primordial spectra also inevitably lead to strong amplification of the scalar-induced, secondary gravitational waves (GWs) at higher frequencies. The recent detection of the stochastic gravitational wave background (SGWB) by the pulsar timing arrays (PTAs) has opened up the possibility of directly probing the very early universe. Different studies have shown that, when PBHs are assumed to have been formed during the epoch of radiation domination, the mechanism for the amplification of the scalar-induced GWs that is required to explain the PTA data can overproduce the PBHs over some ranges of masses. In this work, we assume a specific functional form for the primordial scalar power spectrum and examine the production of PBHs and the scalar-induced secondary GWs during the phase of reheating, which precedes the standard epoch of radiation domination. Specifically, we account for the uncertainties in the conditions for the formation of PBHs and ensure that the extent of PBHs produced remains within the observational bounds. We find that the scalar-induced SGWB generated during a phase of reheating with a steeper equation of state (than that of radiation) fit the NANOGrav 15-year data with a stronger Bayesian evidence than the astrophysical scenario involving GWs produced by merging supermassive binary black holes.

We show that quantum fluctuations of an expanding phase transition bubble give rise to gravitational wave (GW) emission, even when considering a single bubble, without bubble collisions or plasma effects. The ratio of GW energy to the total bubble energy reservoir increases with time as ∝t. If the bubble expands for long enough before percolation destroys it, back-reaction due to the GW emission becomes important after t_\rm br∼(16\pi^5) m_\rm pl^2R_0^3, where R_0 is the bubble nucleation radius and m_\rm pl is the reduced Planck mass. As seen by experiments today, the GW energy spectrum would appear blue. However, simple estimates suggest that the signal falls short of detection by even ambitious future experiments.

The null energy condition (NEC) is a cornerstone of general relativity, and its violation could leave observable imprints in the cosmic gravitational wave spectrum. Theoretical models suggest that NEC violations during inflation can amplify the primordial tensor power spectrum, leading to distinct features in the stochastic gravitational wave background (SGWB). In this work, we search for these NEC-violating signatures in the SGWB using data from Advanced LIGO and Advanced Virgo’s first three observing runs. Our analysis reveals no statistically significant evidence of such signals, allowing us to place stringent upper limits on the tensor power spectrum amplitude, P_T,2, during the second inflationary stage. Specifically, we find that P_T,2 ≲0.15 at a 95% confidence level. Notably, this upper limit is consistent with constraints derived from pulsar timing array observations, reinforcing the hypothesis that NEC violations during inflation could explain the signal detected by pulsar timing arrays. Our findings contribute to a deeper understanding of the early Universe and highlight the potential of current and future gravitational wave experiments in probing the physics of inflation and NEC violations.

The null energy condition (NEC) is a fundamental principle in general relativity, and its violation could leave discernible signatures in gravitational waves (GWs). A violation of the NEC during the primordial era would imprint a blue-tilted spectrum on the stochastic gravitational wave background (SGWB) at nanohertz frequencies, potentially accounting for the recently detected signal by pulsar timing arrays. Remarkably, models of NEC violation during inflation also predict a nearly scale-invariant GW spectrum in the millihertz frequency range, which could be detectable by upcoming space- based GW detectors such as Taiji. The observation of this distinctive spectrum would provide compelling evidence for new physics beyond the standard cosmological paradigm. In this study, we explore Taiji’s ability to detect an SGWB arising from NEC violation during inflation, considering various foregrounds and noise sources, including an extragalactic foreground from binary black hole mergers throughout the universe, a galactic foreground from white dwarf binaries, and the intrinsic noise of the Taiji detector. Employing comprehensive Bayesian parameter estimation techniques to analyze simulated Taiji data, we demonstrate a remarkable precision improvement of three orders of magnitude compared to the NANOGrav 15-year data set for measuring the tensor power spectrum amplitude, P_T,2, during the second inflationary stage. This substantial enhancement in measurement capabilities underscores Taiji’s potential as a powerful probe for investigating the NEC violation in the early Universe.

Silk damping is well known in the study of cosmic microwave background (CMB) and accounts for suppression of the angular power spectrum of CMB on large angular multipoles. In this Letter, we study the effect of Silk damping on the scalar- induced gravitational waves (SIGWs). Resulting from the dissipation of cosmic fluid, the Silk damping notably suppresses the energy-density spectrum of SIGWs on scales comparable to a diffusion scale at the decoupling time of feebly- interacting particles. The effect offers a novel observable for probing the underlying particle interaction, especially for those mediated by heavy gauge bosons beyond the standard model of particles. We anticipate that pulsar timing arrays are sensitive to gauge bosons with mass \sim10^3-10^4\,\mathrmGeV, while space- and ground-based interferometers to those with mass \sim10^7-10^12\,\mathrmGeV, leading to essential complements to on-going and future experiments of high-energy physics.

We initiate the LISA template databank for stochastic gravitational wave backgrounds sourced by cosmic strings. We include two templates, an analytical template, which enables more flexible searches, and a numerical template derived directly from large Nambu-Goto simulations of string networks. Using searches based on these templates, we forecast the parameter space within the reach of the experiment and the precision with which their parameters will be reconstructed, provided a signal is observed. The reconstruction permits probing the Hubble expansion and new relativistic DoF in the early universe. We quantify the impact that astrophysical foregrounds can have on these searches. Finally, we discuss the impact that these observations would have on our understanding of the fundamental models behind the string networks. Overall, we prove that LISA has great potential for probing cosmic string models and may reach tensions as low as Gμ=10^-16 - 10^-17 , which translates into energy scales of the order 10^11 \textGeV.

We study thermal and non-thermal resonant leptogenesis in a general setting where a heavy scalar φdecays to right-handed neutrinos (RHNs) whose further out-of-equilibrium decay generates the required lepton asymmetry. Domination of the energy budget of the Universe by the φor the RHNs alters the evolution history of the primordial gravitational waves (PGW), of inflationary origin, which re-enter the horizon after inflation, modifying the spectral shape. The decays of φand RHNs release entropy into the early Universe while nearly degenerate RHNs facilitate low and intermediate scale leptogenesis. We show that depending on the coupling y_R of φto radiation species, RHNs can achieve thermal abundance before decaying, which gives rise to thermal leptogenesis. A characteristic damping of the GW spectrum resulting in two knee-like features or one knee-like feature would provide evidence for low-scale thermal and non-thermal leptogenesis respectively. We explore the parameter space for the lightest right-handed neutrino mass M_1∈[10^2,10^14] GeV and washout parameter K that depends on the light- heavy neutrino Yukawa couplings λ, in the weak (K < 1) and strong (K > 1) washout regimes. The resulting novel features compatible with observed baryon asymmetry are detectable by future experiments like LISA and ET. By estimating signal-to-noise ratio (SNR) for upcoming GW experiments, we investigate the effect of the scalar mass M_φand reheating temperature T_φ, which depends on the φ-N Yukawa couplings y_N.

We analytically calculate the spectrum of stochastic gravitational waves (GWs) emitted by expanding string loops on domain walls in the scenario where domain walls decay by nucleation of string loops. By introducing macroscopic parameters characterizing the nucleation of the loops, the stochastic GW spectrum is derived in a way that is independent of the details of particle physics models. In contrast to GWs emitted from bubble collisions of the false vacuum decay, the string loops do radiate GWs even when they are perfectly circular before their collisions, resulting in that more and more contribution to the spectrum comes from the smaller and smaller loops compared to the typical size of the collided loops. Consequently, the spectrum is linearly proportional to the frequency at the high-frequency region, which is peculiar to this GW source. Furthermore, the results are compared with the recent nano-Hertz pulsar timing array signal, as well as the projected sensitivity curves of future gravitational wave observatories.

In this talk, based on arXiv:2301.11345, arXiv:2305.16388, arXiv:2311.12694, we discuss the production of primordial gravitational waves (GW) sourced by graviton bremsstrahlung during inflationary reheating. For reheating, we consider inflaton decays and annihilations into pairs of bosons or fermions, assuming an inflaton φthat oscillates around a generic monomial potential V(φ) ∝φ^n. The GW spectrum exhibits distinct features depending on the underlying reheating dynamics, which is controlled by the inflaton potential and the type of coupling between the inflaton and the matter fields. We show that the produced stochastic GW background could be probed in next- generation GW detectors, especially at high frequencies. We further highlight the potential of bremsstrahlung-induced GW to probe the underlying dynamics of reheating.

Cosmic strings are a common prediction in many grand unified theories and a promising source of stochastic gravitational waves (GWs) from the early Universe. In this paper, we point out that the GW signal from cosmic strings produced at a comparatively low energy scale, v ≲10^9 \textrmGeV, exhibits several novel features that are not present in the case of high-scale cosmic strings. Our findings notably include (i) a sharp cutoff frequency f_\rm cut in the GW spectrum from the fundamental oscillation mode on closed string loops and (ii) an oscillating pattern in the total GW spectrum from all oscillation modes whose local minima are located at integer multiples of f_\rm cut. These features reflect the fact that string loops produced in the early Universe fail to shrink to zero size because of GW emission within the age of the Universe, if their tension is low enough. In addition, they offer an exciting opportunity to directly probe the discrete spectrum of oscillation modes on closed string loops in GW observations. For strings produced at a scale v ∼10^9\textrmGeV, the novel features in the GW spectrum are within the sensitivity reach of future experiments such as BBO and DECIGO.

The positive evidence of a nano-hertz gravitational wave background recently found by several pulsar timing array (PTA) collaborations opened up a window to test modified gravity theories in a unique frequency band in parallel to other gravitational wave detection experiments. In particular, the overlap reduction function (ORF) in PTA observation is sensitive to the phase velocity of gravitational waves. In this work, we provide analytical expressions for the coefficients of the multipole moments in the ORF, and utilize these analytical results to study constraints on the phase velocity from the frequency dependent overlap reduction function obtained from the Chinese PTA (CPTA) data. While the data contain large error bars yet, interesting constraints are found in the frequency-dependent ORF in the case of subluminal phase velocity. This makes us expect that the nano-hertz band gravitational wave background will become one of the important arenas for exploring modified gravity theories.

Third generation ground-based gravitational wave (GW) detectors, such as Einstein Telescope and Cosmic Explorer, will operate in the (\textfew-10^4) Hz frequency band, with a boost in sensitivity providing an unprecedented reach into primordial cosmology. Working concurrently with pulsar timing arrays in the nHz band, and LISA in the mHz band, these 3G detectors will be powerful probes of beyond the standard model particle physics on scales T≳10^7GeV. Here we focus on their ability to probe phase transitions (PTs) in the early universe. We first overview the landscape of detectors across frequencies, discuss the relevance of astrophysical foregrounds, and provide convenient and up-to-date power-law integrated sensitivity curves for these detectors. We then present the constraints expected from GW observations on first order PTs and on topological defects (strings and domain walls), which may be formed when a symmetry is broken irrespective of the order of the phase transition. These constraints can then be applied to specific models leading to first order PTs and/or topological defects. In particular we discuss the implications for axion models, which solve the strong CP problem by introducing a spontaneously broken Peccei-Quinn (PQ) symmetry. For post-inflationary breaking, the PQ scale must lie in the 10^8-10^11 GeV range, and so the signal from a first order PQ PT falls within reach of ground based 3G detectors. A scan in parameter space of signal-to-noise ratio in a representative model reveals their large potential to probe the nature of the PQ transition. Additionally, in heavy axion type models domain walls form, which can lead to a detectable GW background. We discuss their spectrum and summarise the expected constraints on these models from 3G detectors, together with SKA and LISA.

The circular polarization of the stochastic gravitational wave background (SGWB) is a key observable for characterising the origin of the signal detected by Pulsar Timing Array (PTA) collaborations. Both the astrophysical and the cosmological SGWB can have a sizeable amount of circular polarization, due to Poisson fluctuations in the source properties for the former, and to parity violating processes in the early universe for the latter. Its measurement is challenging since PTA are blind to the circular polarization monopole, forcing us to turn to anisotropies for detection. We study the sensitivity of current and future PTA datasets to circular polarization anisotropies, focusing on realistic modelling of intrinsic and kinematic anisotropies for astrophysical and cosmological scenarios respectively. Our results indicate that the expected level of circular polarization for the astrophysical SGWB should be within the reach of near future datasets, while for cosmological SGWB circular polarization is a viable target for more advanced SKA-type experiments.

Pulsar Timing Array projects have found evidence of a stochastic background of gravitational waves (GWB) using data from an ensemble of pulsars. In the literature, minimal assumptions are made about the signal and noise processes that affect data from these pulsars, such as pulsar spin noise. These assumptions are encoded as uninformative priors in Bayesian searches, though Frequentist approaches make similar assumptions. Uninformative priors are not suitable for (noise) properties of pulsars in an ensemble, and they bias estimates of model parameters such as gravitational-wave signal parameters. Both Frequentist and Bayesian searches are affected. In this letter, more appropriate priors are proposed in the language of Hierarchical Bayesian Modeling, where the properties of the ensemble of pulsars are jointly described with the properties of the individual components of the ensemble. Results by Pulsar Timing Array projects should be re-evaluated using Hierarchical Models.

The existence of a primordial stochastic gravitational wave background (SGWB) is a common prediction in various models of the early Universe. Despite constraints at different frequency ranges and claims of detection in the nHz range by Pulsar Timing Arrays, the amplitude and spectral dependence of the SGWB in the mHz range remain largely unknown. Plausible models of early Universe Physics predict a wide range of SGWB amplitudes, from undetectable to exceeding the constraints from Big Bang Nucleosynthesis. This paper explores the potential impact of a prominent primordial SGWB on LISA’s main scientific targets. Our main analyses focuses on Massive Black Hole Binaries (MBHBs). By employing publicly available MBHB population models and state-of-the-art LISA’s forecasting pipeline, we analyze the effects of the SGWB on MBHB detections. We find that the decrease in the signal-to-noise ratio induced by a strong primordial GWB can significantly reduce the number of detectable events, compromise the precision of constraints, and even hinder sky localization for some events. We also examine the impact of the SGWB on Stellar Origin Black Hole Binaries (SOBHBs) and Galactic Binaries (GBs), which are fainter sources than MBHBs. Depending on the spectral properties of the SGWB, we conclude that these sources could be either marginally affected or rendered completely undetectable. This largely unexplored aspect raises critical questions about the potential challenges posed by a prominent SGWB to LISA’s astrophysical objectives, including MBHBs, SOBHBs, and GBs.

Employing the publicly available CosmoLattice code, we conduct numerical simulations of a domain wall network and the resulting gravitational waves (GWs) in a radiation-dominated Universe in the Z_2-symmetric scalar field model. In particular, the domain wall evolution is investigated in detail both before and after reaching the scaling regime, using the combination of numerical and theoretical methods. We demonstrate that the total area of closed walls is negligible compared to that of a single long wall stretching throughout the simulation box. Therefore, the closed walls are unlikely to have a significant impact on the overall network evolution. This is in contrast with the case of cosmic strings, where formation of loops is crucial for maintaining the system in the scaling regime. To obtain the GW spectrum, we develop a technique that separates physical effects from numerical artefacts arising due to finite box size and non-zero lattice spacing. Our results on the GW spectrum agree well with Refs. [29, 30], which use different codes. Notably, we observe a peak at the Hubble scale, an exponential falloff at scales shorter than the wall width, and a plateau/bump at intermediate scales. We also study sensitivity of obtained results on the choice of initial conditions. We find that different types of initial conditions lead to qualitatively similar domain wall evolution in the scaling regime, but with important variations translating into different intensities of GWs.

Primordial gravitational waves have crucial implications for the origin of the universe and fundamental physics. Using currently available cosmic microwave background data from Planck, ACT and SPT separately or their combinations with BK18 B-mode polarization and DESI observations, we give the strongest constraints on primordial gravitational waves so far.

The growing tensions between the early Universe and the late Universe increasingly highlight the importance of developing precise probes for late cosmology. As significant late-Universe probes, Type Ia supernovae (SNe Ia) and gravitational waves (GWs) can provide measurements of relative and absolute distances, respectively. Their complementary nature is likely to break the degeneracies among cosmological parameters, thereby yielding more precise constraints. In this study, we use 43 gravitational-wave sources from the Third LIGO-Virgo-KAGRA Gravitational-Wave Transient Catalog (GWTC-3) and 1590 SNe Ia from Pantheon+ compilation to constrain the dark energy models, as an attempt to achieve precise late-Universe cosmological constraints. For the dark siren GW event, we estimate the corresponding redshift using the binary black hole redshift distribution model. The combination of GW and SNe Ia data could provide the precision on the Hubble constant (H0) and the present matter density (Omega_m) of approximately 20% and 8% for the LambdaCDM model. If we consider the equation of state of dark energy (w), the combination sample constrains the precision of w to approximately 30%. Although the combination of GW and SNe Ia observations effectively breaks degeneracies among various cosmological parameters, yielding more stringent constraints, the precision of these constraints still does not meet the stringent standards required by precision cosmology. However, it is reasonable to anticipate that, in the near future, the joint observations of GWs and SNe Ia will become a powerful tool, particularly in the late Universe, for the precise measurement of cosmological parameters.

Pulsar timing arrays (PTAs), aimed at detecting gravitational waves (GWs) in the 1∼100 nHz range, have recently made significant strides. Compelling evidence has emerged for a common spectrum signal spatially correlated among pulsars, following a Hellings-Downs (HD) pattern, which is crucial for detecting a gravitational-wave background (GWB). However, the HD curve is expected for discrete and non-interfering sources, which is unlikely to hold in realistic scenarios with potential interference among numerous GW sources, such as the supermassive black-hole binaries. Incorporating interference was previously expected to introduce an irreducible uncertainty (known as "cosmic variance") in discerning the HD correlation; however, our work reveals how this interference generates measurable frequency-dependent spatial correlations distinct from the HD curve. The spatial correlations for interfering sources (referred to as "ISC") still exhibit contributions in the quadrupole and higher orders, resembling the HD correlation and encoding the nature of GW radiations. We apply these novel correlations to search for a GWB in the NANOGrav 15-year data set. In an optimistic estimation, our findings show a Bayes factor of 33.7\pm 3.2 comparing ISC to the HD correlation, and an improvement in optimal statistic signal-to-noise ratio from 4.9\pm 1.1 for the HD correlation to 6.6\pm 1.7 for the ISC, highlighting the significant enhancement in evidence for detecting a GWB through incorporating interference.

One of the key predictions of the standard inflationary paradigm is the quantum mechanical generation of the transverse and traceless tensor fluctuations due to the rapid accelerated expansion of space, which later constitute a stochastic background of primordial gravitational waves (GWs). The amplitude of the (nearly) scale-invariant inflationary tensor power spectrum at large scales provides us with crucial information about the energy scale of inflation in the case of the minimal inflaton coupling to gravity. Furthermore, the spectral energy density, \Omega__\rm GW(f), of the GWs at sufficiently small scales (or, large frequencies f) serves as an important observational probe of post- inflationary primordial dynamics. In fact, the small-scale spectral tilt, n__\rm GW = \frac\rm d\log\Omega__\rm GW\rm d\logf, of the spectral energy density of GWs is sensitive to the (unknown) post-inflationary equation of state (EoS), w, of the universe; with a softer EoS (w < 1/3) leading to a red tilt: n__\rm GW < 0, while a stiffer EoS (w > 1/3) resulting in a blue tilt: n__\rm GW > 0. The post-inflationary dynamics, however, is generically expected to be quite complex, potentially involving a number of distinct phases. Hence, in this work, we discuss the possibility of multiple sharp transitions, namely w_1 \to w_2 \to w_3 \to ... \to w_n, in the EoS of the post-inflationary universe and compute the corresponding spectral energy density of the inflationary GWs. We explicitly determine the region of the parameter space \lbrace w_1,  w_2,  w_3, ..., w_n\rbrace which leads to a potentially detectable signal in the upcoming GW detectors, without violating the current constraints.

Primordial gravitational waves from the very early stages of the universe, such as inflation or bounce processes, are an irreducible cosmological source of the stochastic gravitational wave background (SGWB). The recent detection of SGWB signals around the nano-Hertz frequency by pulsar timing arrays (PTAs), including NANOGrav, EPTA, PPTA, IPTA, and CPTA, opens a new window to explore these very early stages of the universe through these primordial gravitational waves. In this work, we investigate the generation and evolution of primordial gravitational waves in a generic big bounce cosmology by parameterizing its background evolution into four phases, where perturbation modes exit and re- enter the horizon twice. By analytically solving the equation of motion for primordial gravitational waves and matching solutions at the boundaries, we obtain the explicit form of the primordial gravitational wave spectrum in a generic big bounce cosmology. We find that, according to the evolution of primordial gravitational waves, a generic scenario of big bounce cosmology can be categorized into four distinct types. We introduce four toy models for these categories, demonstrating that our analytical results can be straightforwardly applied to various bouncing universe models in which the equation of state of the background is constant in each phase. We also prospect future applications of our results in interpreting SGWB signals searched by PTAs and upcoming advanced gravitational wave detectors such as SKA, Taiji, Tianqin, LISA, DECIGO, and aLIGO/Virgo/KAGRA using Bayesian analysis.

Recent data seem to suggest a preference for the evolving dark energy (DE). However, if the case is actually so, and not caused by unknown systematics in data, it might impact our understanding about our Universe in an anomalous way due to the shifts of some primary parameters. As an example, we present the search for the primordial gravitational waves, based on the evolving DE. The joint analysis of recent BICEP/Keck cosmic microwave background (CMB) B-mode polarization data with Planck18 CMB, DESI baryon acoustic oscillations and PantheonPlus data shows that the bestfit tensor-to-scalar ratio is r_0.05∼0.01, and the lower bound of r_0.05 is ∼2σnon-zero.

We propose Fast Radio Burst (FRB) timing, which uses the precision measurements of the arrival time differences of repeated FRB signals along multiple sightlines, as a new probe of gravitational waves (GWs) around nHz to \muHz frequencies, with the highest frequency limited by FRB repeating period. The anticipated experiment requires a sightline separation of tens of AU, achieved by sending radio telescopes to space. We find the signal of arrival time difference induced by GWs depends only on the local GWs in the solar system and we can correlate the measurements from different FRB sources or the same source with different repeaters, which leads to a better sensitivity with a larger number of FRB repeaters detected. The projected sensitivity shows this method is a competitive probe in the nHz to \muHz frequency range. It can fill the ’\muHz gap’ between pulsar timing arrays and Laser Interferometer Space Antenna (LISA) and is complementary to other proposals of GW detection in this frequency band.

A large primordial lepton asymmetry can lead to successful baryogenesis by preventing the restoration of electroweak symmetry at high temperatures, thereby suppressing the sphaleron rate. This asymmetry can also lead to a first-order cosmic QCD transition, accompanied by detectable gravitational wave (GW) signals. By employing next-to-leading order dimensional reduction we determine that the necessary lepton asymmetry is approximately one order of magnitude smaller than previously estimated. Incorporating an updated QCD equation of state that harmonizes lattice and functional QCD outcomes, we pinpoint the range of lepton flavor asymmetries capable of inducing a first-order cosmic QCD transition. To maintain consistency with observational constraints from the Cosmic Microwave Background and Big Bang Nucleosynthesis, achieving the correct baryon asymmetry requires entropy dilution by approximately a factor of ten. However, the first-order QCD transition itself can occur independently of entropy dilution. We propose that the sphaleron freeze-in mechanism can be investigated through forthcoming GW experiments such as \muAres.

One of the fundamental characteristics of slow roll inflation is its generation of tensor perturbations, which manifest as stochastic gravitational waves (GWs). Slow roll inflation results in a nearly scale-invariant GW spectrum that maintains its scale invariance as it transitions into the radiation-dominated era. However, introducing an intermediate reheating phase can modify the spectral tilt, depending on the equation of state governing that particular epoch. These GWs, especially on smaller scales, are anticipated to be observable by forthcoming GW detectors. In this study, we initially delineate the parameter space encompassing the inflationary energy scale, reheating temperature, and equation of state in a model-independent manner, focusing on the spectra detectable by GW detectors such as LISA, ET, DECIGO, and BBO. We also examine the implications for the α-attractor model of inflation and explore the observational constraints on n_s-r prediction in the light of GW detection. Then, we point out the probable ranges for various non-gravitational and gravitational coupling between the inflaton and Standard Model particles considering the perturbative reheating. If one assumes PBHs were formed during the early reheating era, such detection of GW signal also sheds light on the probing PBH parameters. Note that for the case of PBH domination, we also consider the contribution of the induced GWs due to the density fluctuation in PBH distribution, which helps to decode the phase of early PBH domination. Finally, to test the production of other cosmological relics through future GW missions, we consider dark matter produced via gravitational interaction in the early universe.

This review is focused on tests of Einstein’s theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein’s theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves are allowing us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical \emphextreme gravity regime. Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and gravitational fields are large and dynamical. This review begins with the theoretical basis and the predicted gravitational-wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational-wave interferometers and pulsar-timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review then discusses gravitational-wave tests using compact binary systems, and ends with a description of the first gravitational wave observations by advanced LIGO, the stochastic gravitational wave background observations by pulsar timing arrays, and the tests that can be performed with them..

The NANOGrav 15-year data provides compelling evidence for a stochastic gravitational-wave (GW) background at nanohertz frequencies. The simplest model- independent approach to characterizing the frequency spectrum of this signal consists in a simple power-law fit involving two parameters: an amplitude A and a spectral index γ. In this paper, we consider the next logical step beyond this minimal spectral model, allowing for a running (i.e., logarithmic frequency dependence) of the spectral index, \gamma_run(f) = γ+ β\ln(f/f_ref). We fit this running-power-law (RPL) model to the NANOGrav 15-year data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameter βconsistent with no running, β∈[-0.80,2.96], and an inconclusive Bayes factor, B(RPL vs. CPL) = 0.69 +- 0.01. We thus conclude that, at present, the minimal CPL model still suffices to adequately describe the NANOGrav signal; however, future data sets may well lead to a measurement of nonzero β. Finally, we interpret the RPL model as a description of primordial GWs generated during cosmic inflation, which allows us to combine our results with upper limits from big-bang nucleosynthesis, the cosmic microwave background, and LIGO- Virgo-KAGRA.

We consider the effects of relaxing the assumption that gravitational waves composing the stochastic gravitational wave background (SGWB) are uncorrelated between frequencies in analyses of the data from Pulsar Timing Arrays (PTAs). While individual monochromatic plane waves are often a good approximation, a background composed of unresolved astrophysical sources cannot be exactly uncorrelated since an infinite plane wave propagates no temporal signal. We consider how relaxing this assumption allows us to extract potential information about modified dispersion relations and other fundamental physics questions, as both the group and phase velocity of waves become relevant. After developing the formalism we carry out simple Gaussian wavepacket examples and then consider more realistic waveforms, such as that from binary inspirals. When the frequency evolves only slowly across the PTA temporal baseline, the monochromatic assumption at an effective mean frequency remains a good approximation and we provide scaling relations that characterize its accuracy.

As pulsar timing arrays (PTAs) transition into the detection era of the stochastic gravitational wave background (GWB), it is important for PTA collaborations to review and possibly revise their observing campaigns. The detection of a ”single source” would be a boon for gravitational astrophysics, as such a source would emit gravitational waves for millions of years in the PTA frequency band. Here we present generic methods for studying the effects of various observational strategies, taking advantage of detector sensitivity curves, i.e., noise-averaged, frequency-domain detection statistics. The statistical basis for these methods is presented along with myriad examples of how to tune a detector towards single, deterministic signals or a stochastic background. We demonstrate that trading observations of the worst pulsars for high cadence campaigns on the best pulsars increases sensitivity to single sources at high frequencies while hedging losses in GWB and single source sensitivity at low frequencies. We also find that sky-targeted observing campaigns yield minimal sensitivity improvements compared with other PTA tuning options. Lastly, we show the importance of the uncorrelated half of the GWB, i.e. the pulsar-term, as an increasingly prominent sources of noise and show the impact of this emerging noise source on various PTA configurations.

Future space-based interferometers offer an unprecedented opportunity to detect signals from the stochastic gravitational wave background originating from a first-order phase transition at the electroweak scale. The phase transition is accompanied by a change of the equation of state from that of pure radiation. In this work we study the effect of this change on the power spectrum of gravitational waves generated by the sound waves in the plasma during the acoustic phase of the transition. We carry out an analytic calculation assuming that the sound speed and the fluid shear-stress that sources tensor perturbations remain approximately constant during the acoustic phase. The effect of a softer equation of state is twofold: (i) a scale-independent suppression of the power spectrum at all scales, due to the modified propagation of both sound and gravitational waves and (ii) the peak of the spectrum moves to smaller frequencies as the equation of state becomes softer. The power-law indices of the spectrum at small and large scales are unaffected by the softening of the equation of state. Our work improves the current estimation of the gravitational waves power spectrum from first order phase transitions and expands the possible scenarios of transitions that can be tested by gravitational wave detectors.

The gravitational wave (GW) interferometers LISA and ET are expected to be functional in the next decade(s), possibly around the same time. They will operate over different frequency ranges, with similar integrated sensitivities to the amplitude of a stochastic GW background (SGWB). We investigate the synergies between these two detectors, in terms of a multi-band detection of a cosmological SGWB characterised by a large amplitude, and a broad frequency spectrum. By investigating various examples of SGWBs, such as those arising from cosmological phase transition, cosmic string, primordial inflation, we show that LISA and ET operating together will have the opportunity to assess more effectively the characteristics of the GW spectrum produced by the same cosmological source, but at separate frequency scales. Moreover, the two experiments in tandem can be sensitive to features of early universe cosmic expansion before big-bang nucleosynthesis (BBN), which affects the SGWB frequency profile, and which would not be possible to detect otherwise, since two different frequency ranges correspond to two different pre-BBN (or post- inflationary) epochs. Besides considering the GW spectrum, we additionally undertake a preliminary study of the sensitivity of LISA and ET to soft limits of higher order tensor correlation functions. Given that these experiments operate at different frequency bands, their synergy constitutes an ideal direct probe of squeezed limits of higher order GW correlators, which can not be measured operating with a single instrument only.

We study the generation of gravitational waves (GWs) during a cosmological first-order phase transition (PT) using the recently introduced Higgsless approach to numerically simulate the fluid motion induced by the PT. We present for the first time GW spectra sourced by bulk fluid motion in the aftermath of strong first-order PTs (α= 0.5), alongside weak (α= 0.0046) and intermediate (α= 0.05) PTs, previously considered in the literature. We find that, for intermediate and strong PTs, the kinetic energy in our simulations decays, following a power law in time. The decay is potentially determined by non-linear dynamics and hence related to the production of vorticity. We show that the assumption that the source is stationary in time, characteristic of compressional motion in the linear regime (sound waves), agrees with our numerical results for weak PTs, since in this case the kinetic energy does not decay with time. We then provide a theoretical framework that extends the stationary assumption to one that accounts for the time evolution of the source: as a result, the GW energy density is no longer linearly increasing with the source duration, but proportional to the integral over time of the squared kinetic energy fraction. This effectively reduces the linear growth rate of the GW energy density and allows to account for the period of transition from the linear to the non-linear regimes of the fluid perturbations. We validate the novel theoretical model with the results of simulations and provide templates for the GW spectrum for a broad range of PT parameters.

We investigate the phenomenon of gravitational baryogenesis within the context of a specific modified theory of gravity, namely, energy-momentum squared gravity or f(R, T_μνT^μν) gravity. In this framework, the gravitational Lagrangian is formulated as a general function of the Ricci scalar R and the self-contraction of the energy-momentum tensor, \mathcalT^2 ≡T_μνT^μν. This approach extends the conventional paradigm of gravitational baryogenesis by introducing new dependencies that allow for a more comprehensive exploration of the baryon asymmetry problem. Our analysis aims to elucidate the role of these gravitational modifications in the generation of baryon asymmetry, a critical issue in cosmology that remains unresolved within the Standard Model of particle physics. By incorporating \mathcalT^2 into the gravitational action, we propose that these modifications can significantly influence the dynamics of the early universe, thereby altering the conditions under which baryogenesis occurs. This study not only provides a novel depiction of gravitational baryogenesis but also offers insights into how modified gravity theories can address the longstanding question of baryon asymmetry. The implications of our findings suggest that f(R, T_μνT^μν) gravity could play a crucial role in understanding the fundamental processes that led to the matter-antimatter imbalance observed in the universe today.

Gravitational waves from cosmological phase transitions are novel probes of fundamental physics, making their precise calculation essential for revealing various mysteries of the early Universe. In this work we propose a framework that enables the consistent calculation of such gravitational waves sourced by sound waves. Starting from the Lagrangian, this framework integrates the calculation of the dynamics of first-order phase transitions in a self- consistent manner, eliminating various approximations typically introduced by conventional methods. At the heart of our approach is the congruous evaluation of the phase transition hydrodynamics that, at every step, is consistently informed by the Lagrangian. We demonstrate the application of our framework using the SM+|H|^6 model, deriving the corresponding gravitational wave spectrum. Our framework establishes a robust foundation for the precise prediction of gravitational waves from phase transitions.

This work continues the research presented in the article [1], where we estimate the Gertsenshtein effect’s influence on the long-wavelength part of relic gravitational wave spectrum. Here, the differential equation system for the Gertsenshtein effect in Friedman-LeMaitre-Robertson-Walker universe, derived in [1], is simplified for gravitational waves in the under-horizon regime during radiation dominance epoch. Then, the obtained system is solved analytically. As a result of the solution analysis a conclusion was made about a significant increase of relic GWs with the frequencies k≳10^-11 Hz for magnetic field strength about 1 nGs. In addition, at the end of the article model dependency of the result is discussed

In the summer of 2023, the pulsar timing arrays (PTAs) announced a compelling evidence for the existence of a nanohertz stochastic gravitational wave background (SGWB). Despite this breakthrough, however, several critical questions remain unanswered: What is the source of the signal? How can cosmic variance be accounted for? To what extent can we constrain nanohertz gravity? When will individual supermassive black hole binaries become observable? And how can we achieve a stronger detection? These open questions have spurred significant interests in PTA science, making this an opportune moment to revisit the astronomical and theoretical foundations of the field, as well as the data analysis techniques employed. In this review, we focus on the theoretical aspects of the SGWB as detected by PTAs. We provide a comprehensive derivation of the expected signal and its correlation, presented in a pedagogical manner, while also addressing current constraints. Looking ahead, we explore future milestones in the field, with detailed discussions on emerging theoretical considerations such as cosmic variance, the cumulants of the one- and two-point functions, subluminal gravitational waves, and the anisotropy and polarization of the SGWB.

We study the contribution of large scalar perturbations sourced by a sharp feature during cosmic inflation to the stochastic gravitational wave background (SGWB), extending our previous work to include the SGWB sourced during the inflationary era. We focus in particular on three-field inflation, since the third dynamical field is the first not privileged by the perturbations’ equations of motion and allows a more direct generalization to N-field inflation. For the first time, we study the three-field isocurvature perturbations sourced during the feature and include the effects of isocurvature masses. In addition to a two-field limit, we find that the third field’s dynamics during the feature can source large isocurvature transients which then later decay, leaving an inflationary-era-sourced SGWB as their only observable signature. We find that the inflationary-era signal shape near the peak is largely independent of the number of dynamical fields and has a greatly enhanced amplitude sourced by the large isocurvature transient, suppressing the radiation-era contribution and opening a new window of detectable parameter space with small adiabatic enhancement. The largest enhancements we study could easily violate backreaction constraints, but much of parameter space remains under perturbative control. These SGWBs could be visible in LISA and other gravitational wave experiments, leaving an almost universal signature of sharp features during multi-field inflation, even when the sourcing isocurvature decays to unobservability shortly afterwards.

The symmetron is a light scalar which provides a screening mechanism so as to evade the strong constraints from local gravity tests. In order to achieve this goal, a Z_2 symmetry is imposed on the symmetron model. In this paper, we introduce a new symmetron Chern-Simons-like gravitational interaction which is Z_2 invariant but breaks the parity symmetry explicitly. As a result, it is found that this coupling can generate gravitational wave (GW) amplitude birefringence when GWs propagate over the symmetron backgrounds. Due to the matter density difference, the symmetron profile changes significantly when entering the galaxy, so that we need to discuss the extra-galactic and galactic situations separately. On the one hand, the cosmological symmetron field follows the adiabatic solution, which induces a parity-violating GW amplitude correction with its exponent proportional to the GW frequency and the traveling distance. On the other hand, the symmetron takes the screening solution within the Milky Way, and the generated GW birefringence is only a function of the GW frequency. By further comparing these two contributions, we find that the extra-galactic symmetron field produces the dominant birefringence effects. Finally, with the latest GW data from LIGO-Virgo-Kagra, we place a reasonable constraint on the parity-violating coupling parameter in this symmetron model.

In the milli-Hertz frequency band, stochastic gravitational-wave background can be composed of both astronomical and cosmological sources, both can be anisotropic. Numerically depicting these anisotropies can be critical in revealing the underlying properties of their origins. For the first time, we perform a theoretical analysis of the constraining ability of TianQin on multiple moments of the stochastic background. First, we find that with a one- year operation, for a background with a signal-to-noise ratio of 16, TianQin can recover the multiple moments up to l=4. We also identified a unique feature of the stochastic background sky map, which is the mirror symmetry along the fixed orbital plane of TianQin. Thirdly, we explain the difference in anisotropy recovering ability between TianQin and LISA, by employing the criteria of the singularity of the covariance matrix (which is the condition number). Finally, we find that since the different data channel combinations correspond to different singularities, certain combinations might have an advantage in stochastic background map-making. We believe that the findings of this work can provide an important reference to future stochastic background analysis pipelines. It can also serve as a guideline for designing better gravitational- wave detectors aiming to decipher anisotropies in the stochastic background.

We calculate the gravitational wave spectrum generated by sound waves during a cosmological phase transition, incorporating several advancements beyond the current state-of-the-art. Rather than relying on the bag model or similar approximations, we derive the equation of state directly from the effective potential. This approach enables us to accurately determine the hydrodynamic quantities, which serve as initial conditions in a generalised hybrid simulation. This simulation tracks the fluid evolution after bubble collisions, leading to the generation of gravitational waves. Our work is the first self- consistent numerical calculation of gravitational waves for the real singlet extension of the standard model. Our computational method is adaptable to any particle physics model, offering a fast and reliable way to calculate gravitational waves generated by sound waves. With fewer approximations, our approach provides a robust foundation for precise gravitational wave calculations and allows for the exploration of model-independent features of gravitational waves from phase transitions.

We search for a stochastic gravitational-wave background (SGWB) originating from scalar-induced gravitational waves (SIGWs) with the sound speed resonance (SSR) effect using data from Advanced LIGO and Advanced Virgo’s first three observing runs. The SSR mechanism, characterized by an oscillating sound speed squared term, can induce a nonperturbative parametric amplification of specific perturbation modes during inflation, leading to enhanced primordial curvature perturbations and a significant SIGW signal. We perform a Bayesian analysis to constrain the model parameters describing the SGWB spectrum from the SSR effect. Our results show no statistically significant evidence for the presence of such a signal in the current data. Consequently, we place an upper limit of |\tau_0| ≲5.9 \times 10^3\,\mathrms at 95% confidence level on the start time of the oscillation in the SSR model. These results demonstrate the capability of current gravitational wave detectors to probe inflation models through the SSR mechanism and paves the way for future searches with improved sensitivity.

The recent evidence for a stochastic gravitational wave background (GWB) in the nanohertz band, announced by pulsar timing array (PTA) collaborations around the world, has been posited to be sourced by either a population of supermassive black holes binaries or perturbations of spacetime near the inflationary era, generated by a zoo of various new physical phenomena. Gravitational waves (GWs) from these latter models would be explained by extensions to the standard model of cosmology and possibly to the standard model of particle physics. While PTA datasets can be used to characterize the parameter spaces of these models, energy conservation and limits from the cosmic microwave background (CMB) can be used \textita priori to bound those parameter spaces. Here we demonstrate that taking a simple rule for energy conservation and using CMB bounds on the radiation energy density can set stringent limits on the parameters for these models.

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration has recently reported strong evidence for a signal at nanohertz, potentially the first detection of the stochastic gravitational-wave background (SGWB). We investigate whether the NANOGrav signal is consistent with the SGWB predicted by string cosmology models. By performing Bayesian parameter estimation on the NANOGrav 15-year data set, we constrain the key parameters of a string cosmology model: the frequency f_s and the fractional energy density \Omega_\mathrmgw^s of gravitational waves at the end of the dilaton-driven stage, and the Hubble parameter H_r at the end of the string phase. Our analysis yields constraints of f_s = 1.2^+0.6_-0.6\times 10^-8 \mathrmHz and \Omega_\mathrmgw^s = 2.9^+5.4_-2.3\times 10^-8, consistent with theoretical predictions from string cosmology. However, the current NANOGrav data is not sensitive to the H_r parameter. We also compare the string cosmology model to a simple power-law model using Bayesian model selection, finding a Bayes factor of 2.2 in favor of the string cosmology model. Our results demonstrate the potential of pulsar timing arrays to constrain cosmological models and study the early Universe.

As a space-borne gravitational wave observatory, TianQin can observe a large variety of gravitational wave sources. The rich signals can be composed by different types of astronomical systems, like Galactic compact binaries, inspiral of stellar mass black holes, merger of massive black holes, and extreme mass ratio inspirals. The incoherent summation of these signals can also form a stochastic gravitational wave background. Using the future TianQin observation, it is possible to put stringent constraints on fundamental science, like the expansion history of our universe. In this work, we provide a brief review of these topics that contributes to the 7th International Workshop on the TianQin Science Mission.

The opening of the gravitational wave window has significantly enhanced our capacity to explore the universe’s most extreme and dynamic sector. In the mHz frequency range, a diverse range of compact objects, from the most massive black holes at the farthest reaches of the Universe to the lightest white dwarfs in our cosmic backyard, generate a complex and dynamic symphony of gravitational wave signals. Once recorded by gravitational wave detectors, these unique fingerprints have the potential to decipher the birth and growth of cosmic structures over a wide range of scales, from stellar binaries and stellar clusters to galaxies and large-scale structures. The TianQin space-borne gravitational wave mission is scheduled for launch in the 2030s, with an operational lifespan of five years. It will facilitate pivotal insights into the history of our universe. This document presents a concise overview of the detectable sources of TianQin, outlining their characteristics, the challenges they present, and the expected impact of the TianQin observatory on our understanding of them.

We revisit the presence of primordial gravitational vector modes (V-modes) and their sourcing of primordial magnetic fields (PMF), i.e. magnetogenesis. As the adiabatic vector mode generically decays with expansion, we consider exotic initial conditions which circumvent this issue and lead to observational imprints. The first initial condition is an isocurvature mode between photons and neutrinos vorticities, and the second one is a non-trivial initial condition on the neutrino octupole. Both types of conditions sustain a constant vector mode on super Hubble scales at early times. We also consider a third scenario in which the adiabatic vector modes are rapidly sourced, at a given early but finite time, by an exotic component which develops an anisotropic stress. We find the best fitting parameters in these three cases to CMB and BAO data. We compare the resulting B-mode spectra of the CMB to data from BICEP/Keck and SPTpol. We find that none of the proposed initial conditions can produce large enough PMFs to seed every type of magnetic fields observed. However, V-modes are still consistent with the data and ought to be constrained for a better understanding of the primordial Universe before its hot big-bang phase.

It is straightforward to take the gravitational wave solution to first order in v/c far from a binary source in a Minkowski background and adapt it to the Friedmann-Lemaitre-Robertson-Walker (FLRW) background, representing an expanding isotropic homogeneous universe. We find the analogous solution for a slightly anisotropic background, which may be a more accurate description of our universe, and we use a perturbative form of the Bianchi I metric and demonstrate how the waveform differs. Using supernova anisotropy data as a reference, we show that the assumption of a Bianchi I background could imply a 3.2% difference in inferred luminosity distance compared to what would be inferred under the assumption of the FLRW background. Therefore, the background spacetime used for the inference of the Hubble parameter from gravitational wave data should be considered carefully.

We discuss the theoretical framework behind reconstruction of a generic class of inflationary potentials for canonical single-field slow-roll inflation in a model-independent fashion. The Non-Bunch Davies (NBD) initial condition is an essential choice to determine the structure of potential and to accommodate the blue-tilted tensor power spectrum feature recently observed in NANOGrav. Using the reconstruction technique we found the favoured parameter space which supports blue tilted tensor power spectrum. The validity of the EFT prescription in inflation is also maintained through the use of a new field excursion formula while keeping the necessary and sufficient conditions on the sub-Planckian field values in check. We find that the reconstructed potential display inflection point behaviour, which has deeper connection with high energy physics.

The announcement in the summer of 2023 about the discovery of evidence for a gravitational wave background (GWB) using pulsar timing arrays (PTAs) has ignited both the PTA and the larger scientific community’s interest in the experiment and the scientific implications of its findings. As a result, numerous scientific works have been published analyzing and further developing various aspects of the experiment, from performing tests of gravity to improving the efficiency of the current data analysis techniques. In this regard, we contribute to the recent advancements in the field of PTAs by presenting the most general, agnostic, per-frequency Bayesian search for a low-frequency (red) noise process in these data. Our new method involves the use of a conjugate Jeffrey’s-like multivariate prior which allows one to model all unique parameters of the global PTA-level red noise covariance matrix as a separate model parameter for which a marginalized posterior-probability distribution can be found using Gibbs sampling. Even though perfecting the implementation of the Gibbs sampling and mitigating the numerical stability challenges require further development, we show the power of this new method by analyzing realistic and theoretical PTA simulated data sets. We show how our technique is consistent with the more restricted standard techniques in recovering both the auto and the cross-spectrum of pulsars’ low-frequency (red) noise. Furthermore, we highlight ways to approximately characterize a GWB (both its auto- and cross-spectrum) using Fourier coefficient estimates from single-pulsar and so-called CURN (common uncorrelated red noise) analyses via analytic draws from a specific Inverse-Wishart distribution.

It has been known that stochastic gravitational wave backgrounds (SGWBs) have anisotropies generated by squeezed-type tensor non-Gaussianities originating from scalar-tensor-tensor (STT) and tensor-tensor-tensor cubic interactions. While the squeezed tensor non-Gaussianities in the standard slow-roll inflation with the Bunch-Davies vacuum state are suppressed due to the so-called consistency relation, those in extended models with the violation of the consistency relation can be enhanced. Among such extended models, we consider the inflation model with the non-Bunch-Davies state that has been known to enhance the squeezed tensor non-Gaussianities. We explicitly formulate the primordial STT bispectrum induced during inflation in the context of Horndeski theory with the non-Bunch-Davies state and show that the induced SGWB anisotropies can be enhanced. We then discuss the detectability of those anisotropies in future gravitational wave experiments.

Recent reports of stochastic gravitational wave background from four independent pulsar-timing-array collaborations have renewed the interest in the cosmological gravitational wave background (CGWB), which is expected to open a new window into the early Universe. Although the early Universe is supposed to be extremely flat from an inflationary point of view, the cosmic microwave background (CMB) data alone from the Planck satellite measurement prefers an enhanced lensing amplitude that can be explained by a closed Universe. In this paper, we propose an independent method to constrain the early-universe flatness from the anisotropies of CGWB. Using the generalized harmonic decompositions in the non- flat spacetime, we find CGWBs from different physical mechanisms such as cosmic inflation and phase transitions share the same integrated Sachs-Wolfe (ISW) term but possess different SW terms, which would exhibit different behaviors when including the spatial curvature since the ISW effect is more sensitive to the spatial curvature than the SW effect. Furthermore, we provide the cross- correlations between CGWB and CMB, implying a positive or negative correlation between their SW effect terms depending on the GW mechanisms, which may hint at the sign of f_\mathrmNL when considering non-Gaussianity contributions to anisotropies.

The direct detection of gravitational waves by LIGO has confirmed general relativity (GR) and sparked rapid growth in gravitational wave (GW) astronomy. However, subtle post-Newtonian (PN) deviations observed during the analysis of high signal-to-noise ratio events from the observational runs suggest that standard waveform templates, which assume strict adherence to GR, might overlook signals from alternative theories of gravity. Incorporating these exotic signals into traditional search algorithms is computationally infeasible due to the vast template space required. This paper introduces a proof-of-principle deep learning framework for detecting exotic GW signals, leveraging neural networks trained on GR-based templates. Through their generalization ability, neural networks learn intricate features from the data, enabling the detection of signals that deviate from GR. We present the first study evaluating the capability of deep learning to detect beyond-GR signals, including a variety of PN orders. Our model achieves rapid and accurate identification of exotic GW signals across different luminosity distances, with performance comparable to GR-based detections. In particular, applying the model to the GW150914 event demonstrates excellent performance, highlighting the potential of AI-driven methods for detecting previously overlooked signals beyond GR. This work paves the way for new discoveries in gravitational wave astronomy, enabling the detection of signals that might escape traditional search pipelines.

We summarise the physics of first-order phase transitions in the early universe, and the possible ways in which they might come about. We then focus on gravitational waves, emphasising general qualitative features of stochastic backgrounds produced by early universe phase transitions and the cosmology of their present-day appearance. Finally, we conclude by discussing some of the ways in which a stochastic background might be detected.

We derived here the factor Υ, which quantifies how the gravitational wave spectrum generated by sound waves in the radiation sector grows over time, in a universe with a generic expanding rate set by another dominant energy content. When the dominant energy density satisfies ρ∝a^-3(1+w), we found that Υhas a compact analytical expression: Υ=\frac2[1-y^3(w-1)/2]3(1-w), where y = a(t)/a(t_s) which is the ratio of the scale factor at a later time t to that at t_s when gravitational wave production from sound waves starts. This generic result reduces to that derived previously for radiation-dominated and matter-dominated cases, thus generalizing previous formulas to more general cosmological contexts and providing more accurate results. The derivation relies solely on a stationary source, implying that this generic result of Υserves as an universal factor in describing the growth of the gravitational wave production and can appear beyond cosmological phase transitions.

The nature of the gravitational wave background (GWB) is a key question in modern astrophysics and cosmology, with significant implications for understanding of the structure and evolution of the Universe. We demonstrate how cross-correlating large-scale structure (LSS) tracers with the GWB spatial anisotropies can extract a clear astrophysical imprint from the GWB signal. Focusing on the unresolved population of supermassive black hole binaries (SMBHBs) as the primary source for the GWB at nanohertz frequencies, we construct full-sky maps of galaxy distributions and characteristic strain of the GWB to explore the relationship between GWB anisotropies and the LSS. We find that at current pulsar timing array (PTA) sensitivities, very few loud SMBHBs act as Poisson-like noise. This results in anisotropies dominated by a small number of sources, making GWB maps where SMBHBs trace the LSS indistinguishable from a GWBs from a uniform distribution of SMBHBs. In contrast, we find that the bulk of the unresolved SMBHBs produce anisotropies which mirror the spatial distribution of galaxies, and thus trace the LSS. Importantly, we show that cross-correlations are required to retrieve a clear LSS imprint in the GWB. Specifically, we find this LSS signature can me measured at a 3σlevel in near-future PTA experiments that probe angular scales of \ell_\textmax ≥42, and 5σfor \ell_\textmax ≥72. Our approach opens new avenues to employ the GWB as an LSS tracer, providing unique insights into SMBHB population models and the nature of the GWB itself. Our results motivate further exploration of potential synergies between next-generation PTA experiments and cosmological tracers of the LSS.

We calculate the gravitational waves (GWs) produced by primordial black holes (PBHs) in the presence of the inflaton condensate in the early Universe. Combining the GW production from the evaporation process, the gravitational scattering of the inflaton itself, and the density fluctuations due to the inhomogeneous distribution of PBHs, we propose for the first time a complete coherent analysis of the spectrum, revealing three peaks, one for each source. Three frequency ranges (∼kHz, GHz, and PHz, respectively) are expected, each giving rise to a similar GW peak amplitude \Omega_\rm GW. We also compare our predictions with current and future GWs detection experiments.