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Anisotropic stochastic gravitational wave background (SGWB) serves as a potential probe of the large-scale structure (LSS) of the universe. In this work, we explore the anisotropic SGWB from local ($z < \sim 0.085$) merging stellar mass compact binaries, specifically focusing on merging stellar binary black holes, merging neutron-star-black-hole binaries, and merging binary neutron stars. The analysis employs seven all-sky mock lightcone gravitational wave event catalogues, which are derived from the Millennium simulation combined with a semi-analytic model of galaxy formation and a binary population synthesis model. We calculate the angular power spectra $\mathrm{C}_\ell$ at multipole moments $\ell$, expressed as $\text{log}_{10} [\ell(\ell+1)\mathrm{C}_\ell/(2\pi)]$, based on the skymaps of the overdensity $\delta_\mathrm{GW}$ in the anisotropic SGWB. The spectra for all three source types exhibit an approximately linear increase with $\text{log}_{10} \ell$ at higher $\ell$ (e.g., $\ell > \sim 30 - 300$) in seven catalogues, with a characteristic slope of $\sim 2$. The spectra of seven catalogues exhibit considerable variations, arising from fluctuations in spatial distribution, primarily in the radial distribution, of nearby sources (e.g., $< 50$ Mpc/h). After subtracting these nearby sources, the variations become much smaller and the spectra for the three source types become closely aligned (within discrepancies of a factor of $\sim 2$ across $\ell = 1 - 1000$ for all catalogues)., Comment: 11 pages 5 figures

Gravitational waves (GWs) from core-collapse supernovae (CCSNe) have been proposed as a means to probe the internal physical properties of supernovae. However, due to their complex time-frequency structure, effectively searching for and extracting GW signals from CCSNe remains an unsolved challenge. In this paper, we apply the improved multisynchrosqueezing transform (IMSST) method to reconstruct simulated GW data based on the advanced LIGO (aLIGO) and Einstein Telescope (ET) detectors. These data are generated by the magnetorotational and neutrino-driven mechanisms, and we use the match score as the criterion for evaluating the quality of the reconstruction. To assess whether the reconstructed waveforms correspond to true GW signals, we calculate the false alarm probability of reconstruction (FAPR). For GW sources located at 10 kpc and datasets where the waveform amplitudes are normalized to $5 \times 10^{-21}$ observed by aLIGO, FAPR are $2.1 \times 10^{-2}$ and $6.2 \times 10^{-3}$, respectively. For GW sources at 100 kpc and with waveform amplitudes normalized to $5 \times 10^{-21}$ observed by ET, FAPR are $1.3 \times 10^{-1}$ and $1.5 \times 10^{-2}$, respectively. When the gravitational wave strain reaches $7 \times 10^{-21}$ and the match score threshold is set to 0.75, the IMSST method achieves maximum reconstruction distances of approximately 37 kpc and 317 kpc for aLIGO and ET, respectively. Finally, we compared the performance of IMSST and STFT in waveform reconstruction based on the ET. The results show that the maximum reconstructable distance using STFT is 186 kpc.

We infer the origin channels of hierarchical mergers observed in the LIGO-Virgo-KAGRA (LVK) O1, O2, and O3 runs using a hierarchical Bayesian analysis under a parametric population model. By assuming the active galactic nucleus (ANG) disk and nuclear star cluster (NSC) channels, we find that NSCs likely dominate the hierarchical merger rate in the universe, corresponding to a fraction of $f_{\rm NSC}=0.87_{-0.29}^{+0.10}$ at 90\% credible intervals in our fiducial model; AGN disks may contribute up to nearly half of hierarchical mergers detectable with LVK, specifically $f_{\rm det,AGN}=0.34_{-0.26}^{+0.38}$. We investigate the impact of the escape speed, along with other population parameters on the branching fraction, suggesting that the mass, mass ratio, and spin of the sources play significant roles in population analysis. We show that hierarchical mergers constitute at least $\sim$$10\%$ of the gravitational wave events detected by LVK during the O1-O3 runs. Furthermore, we demonstrate that it is challenging to effectively infer detailed information about the host environment based solely on the distribution of black hole merger parameters if multiple formation channels are considered., Comment: 11 pages, 2 figures, 2 tables, and comments are welcome

Cosmic muon imaging technology is increasingly being applied in various fields. However, simulating cosmic muons typically requires the rapid generation of a large number of muons and tracking their complex trajectories through intricate structures. This process is highly computationally demanding and consumes significant CPU time. To address these challenges, we introduce DeepMuon, an innovative deep learning model designed to efficiently and accurately generate cosmic muon distributions. In our approach, we employ the inverse Box-Cox transformation to reduce the kurtosis of the muon energy distribution, making it more statistically manageable for the model to learn. Additionally, we utilize the Sliced Wasserstein Distance (SWD) as a loss function to ensure precise simulation of the high-dimensional distributions of cosmic muons. We also demonstrate that DeepMuon can accurately learn muon distribution patterns from a limited set of data, enabling it to simulate real-world cosmic muon distributions as captured by detectors. Compared to traditional tools like CRY, DeepMuon significantly increases the speed of muon generation at sea level. Furthermore, we have developed a pipeline using DeepMuon that directly simulates muon distributions in underwater environments, dramatically accelerating simulations for underwater muon radiography and tomography. For more details on our open-source project, please visit https://github.com/wangab0/deepmuon.

The spin characteristics of black holes offer valuable insights into the evolutionary pathways of their progenitor stars, crucial for understanding the broader population properties of black holes. Traditional Hierarchical Bayesian inference techniques employed to discern these properties often entail substantial time investments, and consensus regarding the spin distribution of Binary Black Hole (BBH) systems remains elusive. In this study, leveraging observations from GWTC-3, we adopt a machine learning approach to infer the spin distribution of black holes within BBH systems. Specifically, we develop a Deep Neural Network (DNN) and train it using data generated from a Beta distribution. Our training strategy, involving the segregation of data into 10 bins, not only expedites model training but also enhances the DNN's versatility and adaptability to accommodate the burgeoning volume of gravitational wave observations. Utilizing Monte Carlo-bootstrap (MC-bootstrap) to generate observation-simulated samples, we derive spin distribution parameters: $\alpha=1.3^{+0.25}_{-0.18},\beta=1.70^{+0.24}_{-0.29}$ for the larger BH sample and $\alpha=1.37^{+0.31}_{-0.20},\beta=1.63^{+0.30}_{-0.20}$ for the smaller BH sample. Within our constraints, the distributions of component spin magnitudes suggest the likelihood of both black holes in the BBH merger possessing non-zero spin., Comment: 10 pages, 8 figures, 1 table

Binary stars are as frequency as single stars in the Universe, and at least 70% of the massive stars located in our Galaxy belong to a binary system. We produce the gravitational waveforms for the extreme mass ratio inspiral systems (EMRIs) of binary stars moving around central supermassive black hole (SBH), or called B-EMRIs. We calculate the orbits of such systems via the Hamilton-Jacobi approach. To improve accuracy we adopt the quadrupole-octupole expression of gravitational wave (GW) and study the contribution of radiation reaction. Compared to the waveforms of EMRIs, there are higher frequency oscillations superposed on the waveforms of B-EMRIs. We perform frequency spectrum analysis of the GW waveforms, and find that higher frequency signals give their prominency in the waveforms of B-EMRIs. We study the binary compact objects with different masses and inclination angles of the binary internal orbit plane, and obtain the frequency spectrum variation with respect to the parameters. To obtain more precise result for future observation of GWs from space-based detector, we take into account gravito-electromagnetic (GEM) force for the binary orbit on the equatorial plane, and compare the waveforms with that of EMRIs without GEM force. The result of mismatch shows that the waveforms of B-EMRIs are credibly distinguishable by the space-based GW detectors when GEM force is considered., Comment: 20 pages, 11 figures

General relativity predicts the existence of only two tensorial gravitational wave polarizations, while a generic metric theories of gravity can possess up to four additional polarizations, including two vector and two scalar ones. These vector/scalar polarizations are in general generated by the intrinsic new vector/scalar degrees of freedom of the specific theories of gravity. In this paper, we show that, with the violation of the Lorentz symmetry in the framework of the standard model extension, the additional nontensorial polarizations can be directly excited by the two tensorial degrees of freedom. We consider the diffeomorphism invariant standard model extension in the gravity sector with the Lorentz-violating coefficients $\hat{\boldsymbol s}^{(d)\mu\rho\nu\sigma}$ of the even mass dimension $d\ge4$. In addition to the extra polarizations induced by the tensor modes, the gravitational wave in this theory travels at a speed depending on the propagation direction, experiences dispersion if and only if $d\ge6$, and possesses neither velocity nor amplitude birefringence. The excitement of the extra polarizations is also chiral. The antenna pattern functions of interferometers due to such kind of gravitational waves are generally linear combinations of those for all polarizations. Detected by pulsar timing arrays and the Gaia satellite, the stochastic gravitational wave background in this model could induce couplings among cross correlations, of the redshifts of photons and the astrometric deflections of the positions of pulsars, for different polarizations. These characteristics enable the use of interferometers, pulsar timing arrays and Gaia mission to constrain this model., Comment: 14 pages, 6 figures. Modified according to Referee report

Resolving individual gravitational waves from tens of millions of double white dwarf (DWD) binaries in the Milky Way is a challenge for future space-based gravitational wave detection programs. By using previous data to define the priors for the next search, we propose an accelerated approach of searching the DWD binaries and demonstrate its efficiency based on the GBSIEVER detection pipeline. Compared to the traditional GBSIEVER method, our method can obtain $\sim 50\%$ of sources with 2.5\% of the searching time for LDC1-4 data. In addition, we find that both methods have a similar ability to detect the Milky Way structure by their confirmed sources. The relative error of distance and chirp mass is about 20\% for DWD binaries whose gravitational wave frequency is higher than $4\times10^{-3}$ Hz, even if they are close to the Galactic center. Finally, we propose a signal-to-noise ratio (SNR) threshold for LISA to confirm the detection of DWD binaries. The threshold should be 16 when the gravitational wave frequency is lower than $4\times10^{-3}$ Hz and 9 when the frequency range is from $4\times10^{-3}$ Hz to $1.5\times10^{-2}$ Hz., Comment: 16 pages, 19 figures

The gravitational waves (GW) from core-collapse supernovae (CCSN) have been proposed as a probe to investigate physical properties inside of the supernova. However, how to search and extract the GW signals from core-collapse supernovae remains an open question due to its complicated time-frequency structure. In this paper, we apply the Ensemble Empirical Mode Decomposition (EEMD) method to decompose and reconstruct simulated GW data generated by magnetorotational mechanism and neutrino-driven mechanism within the advanced LIGO, using the match score as the criterion for assessing the quality of the reconstruction. The results indicate that by decomposing the data, the sum of the first six intrinsic mode functions (IMFs) can be used as the reconstructed waveform. To determine the probability that our reconstructed waveform corresponds to a real GW waveform, we calculate the false alarm probability of reconstruction (FAPR). By setting the threshold of the match score to be 0.75, we obtain FAPR of GW sources at a distance of 5 kpc and 10 kpc to be $6\times10^{-3}$ and $1\times10^{-2}$ respectively. If we normalize the maximum amplitude of the GW signal to $5\times10^{-21}$, the FAPR at this threshold is $4\times10^{-3}$. Furthermore, in our study, the reconstruction distance is not equivalent to the detection distance. When the strain of GW reaches $7 \times 10^{-21}$, and the match score threshold is set at 0.75, we can reconstruct GW waveform up to approximately 36 kpc., Comment: 9 pages, 6 figures. Accepted by MNRAS

The Johannsen black hole (BH) is a generic rotating BH admitting three constants of motions (energy, angular momentum, and Carter constant) and is characterized by four deviation parameters besides mass and spin, which could be a model-independent probe of the no-hair theorem. We systematically study the dynamics of null particles around Johannsen BH, revealing the effects of the deviation parameters on the BH shadow as well as the effects of spin. By using the shadow boundaries of M87* and SgrA*, for the first time, the deviation parameters of those BHs are constrained. The detailed results depend on the spin $a$ and inclination angle $ \theta_0$. Assuming $a=0.2$ and $\theta_0=15^{\circ}$, the deviation parameter $\alpha_{13}$ are constained within $\sim $ [-3.5, 6] for M87* observation and [-3, 0.5] for SgrA* observation. We also show the images of a Johannsen BH surrounded by a Page-Thorne thin accretion disk observed by a remote observer with a ray-tracing method and discuss the effects of the deviation parameters on deforming the accretion disk image, which could be tested by observations with higher sensitivities in the future., Comment: 20 pages, 9 figures

The nature of the merger remnant of binary neutron star (BNS) remains an open question. From the theoretical point of view, one possible outcome is a supra-massive neutron star (SMNS), which is supported by rigid rotation and through its survival of hundreds of seconds before collapsing into a black hole (BH). If this is the case, the SMNS can emit continuous gravitational waves (GW) and electromagnetic (EM) radiation, particularly in the X-ray band. In this work, the ellipticity and initial frequency of SMNS are constrained with a Bayesian framework using simulated X-ray and GW signals, which could be detected by The Transient High Energy Sky and Early Universe Surveyor (THESEUS) and Einstein Telescope (ET), respectively. We found that only considering the X-ray emission can not completely constrain the initial frequency and ellipticity of the SMNS, but it can reduce the ranges of the parameters. Afterwards, we can use the posterior distribution of the X-ray parameter estimates as a prior for the GW parameter estimates. It was found that the 95$\%$ credible region of the joint X-ray-GW analysis was about $10^5$ times smaller than that of the X-ray analysis alone., Comment: Accepted by MNRAS

An enormous number of compact binary systems, spanning from stellar to supermassive levels, emit substantial gravitational waves during their final evolutionary stages, thereby creating a stochastic gravitational wave background (SGWB). We calculate the merger rates of stellar compact binaries and massive black hole binaries using a semi-analytic galaxy formation model -- Galaxy Assembly with Binary Evolution (GABE) in a unified and self-consistent approach, followed by an estimation of the multi-band SGWB contributed by those systems. We find that the amplitudes of the principal peaks of the SGWB energy density are within one order of magnitude $\Omega_{GW} \sim 10^{-9}- 10^{-8}$. This SGWB could easily be detected by the Square Kilometre Array (SKA), as well as planned interferometric detectors, such as the Einstein Telescope (ET) and the Laser Interferometer Space Antenna (LISA). The energy density of this background varies as $\Omega_{GW} \propto f^{2/3}$ in SKA band. The shape of the SGWB spectrum in the frequency range $\sim[10^{-4}$,$1]$Hz could allow the LISA to distinguish the black hole seed models. The amplitude of the SGWB from merging stellar binary black holes (BBHs) at $\sim 100$ Hz is approximately 10 and 100 times greater than those from merging binary neutron stars (BNSs) and neutron-star-black-hole (NSBH) mergers, respectively. Note that, since the cosmic star formation rate density predicted by GABE is somewhat lower than observational results by $\sim 0.2$ dex at z < $\sim 2$, the amplitude of the SGWB in the frequency range $\sim[1$, $10^{4}]$ Hz may be underestimated by a similar factor at most., Comment: 12 pages, 5 figures

String cosmology models predict a relic background of gravitational-wave (GW) radiation in the early universe. The GW energy spectrum of radiated power increases rapidly with the frequency, and therefore it becomes a potential and meaningful observation object for high-frequency GW detector. We focus on the stochastic background generated by superinflation in string theory and search for such signal in the observing data of Advanced LIGO and Virgo O1$\sim$O3 runs in a Bayesian framework. We do not find the existence of the signal, and thus put constraints on the GW energy density. Our results indicate that at $f=100\,\text{Hz}$, the fractional energy density of GW background is less than $1.7\times10^{-8}$ and $2.1\times10^{-8}$ for dilaton-string and dilaton only cases respectively, and further rule out the parameter space restricted by the model itself due to the non-decreasing dilaton and stable cosmology background ($\beta$ bound)., Comment: Accepted by Journal of Cosmology and Astroparticle Physics

The various materials of test masses, and the difference of arm lengths of global ground-based gravitational-wave interferometer detectors offer a unique approach to test Newton's second law, weak equivalence principle, and Einstein equivalence principle with dynamical space-time effects in terms of the interaction of gravitational waves with detectors. We proposed a novel test strategy for the interaction between gravitational waves and detectors, which is independent of particular gravitation theory. A new population level of the Fisher-Matrix approach for multiple sources and multiple detectors case is formalized to evaluate the prospects for a binary neutron star and binary black hole coalescences. Through a generalized detector response, we found more sources could break the parameter degeneracy and one could constrain the interaction and gravitational-inertial mass ratio parameters with the standard deviation $\ls 1\%$ with about 10 compact binary coalescence sources with future third-generation detectors network., Comment: 5 pages, 2 figure

Gravitational lensing has long been used to measure or constrain cosmology models. Although the lensing effect of gravitational waves has not been observed by LIGO/Virgo, it is expected that there can be a few to a few hundreds lensed events to be detected by the future Japanese space-borne interferometers DECIGO and B-DECIGO, if they are running for 4 years. Given the predicted lensed gravitational wave events, one can estimate the constraints on the cosmological parameters via the lensing statistics and the time delay methods. With the lensing statistics method, the knowledge of the lens redshifts, even with the moderate uncertainty, will set the tight bound on the energy density parameter $\Omega_M$ for matter, that is, $0.288\lesssim\Omega_M\lesssim0.314$ at best. The constraint on the Hubble constant $H_0$ can be determined using the time delay method. It is found out that at $5\sigma$, $|\delta H_0|/H_0$ ranges from $3\%$ to $11\%$ for DECIGO, and B-DECIGO will give less constrained results, $8\%-15\%$. In this work, the uncertainties on the luminosity distance and the time delay distance are set to be $10\%$ and $20\%$, respectively. The improvement on measuring these distances will tighten the bounds., Comment: 11 pages, 13 figures. Revised according to Referee's comments

In the near future, the redshift drift observations in optical and radio bands will provide precise measurements on $H(z)$ covering the redshift ranges of $2

The coherent nature of gravitational wave emanating from a compact binary system makes it possible to detect some interference patterns in two (or more) signals registered simultaneously by the detector. Gravitational lensing effect can be used to bend trajectories of gravitational waves, which might reach the detector at the same time. Once this happens, a beat pattern may form, and can be used to obtain the luminosity distance of the source, the lens mass, and cosmological parameters such as the Hubble constant. Crucial question is how many such kind of events could be detected. In this work, we study this issue for the future space-borne detectors: DECIGO and its downscale version, B-DECIGO. It is found out that there can be a few tens to a few hundreds of lensed gravitational wave events with the beat pattern observed by DECIGO and B-DECIGO per year, depending on the evolution scenario leading to the formation of double compact objects. In particular, black hole-black hole binaries are dominating population of lensed sources in which beat patterns may reveal. However, DECIGO could also register a considerable amount of lensed signals from binary neutron stars, which might be accompanied by electromagnetic counterparts. Our results suggest that, in the future, lensed gravitational wave signal with the beat pattern could play an important role in cosmology and astrophysics., Comment: 15 pages, 7 figures. Revised based on Referee's comments

The gravitational wave, traveling a long cosmological distance to reach interferometers, interacts with the (homogeneous and isotropic) cosmological background, so generally speaking, its amplitude and phase are modified in some nontrivial way. As the sensitivity of interferometers is improved, one may detect corrections to the short-wavelength approximation, which naturally includes the information of cosmological evolution. In this work, the Newman-Penrose variable $\Psi_4$ has been calculated to show that there are two new corrections to the short-wavelength approximation. One formally occurs at the first post-Newtonian order but is highly suppressed by the Hubble parameters; the other occurs at the fifth post-Newtonian order, which is due to the variation of the amplitude. The first correction contains the evolution of the Universe, but it may not be easily detected. The second one indicates that the short-wavelength approximation has to be corrected, when the more accurate waveforms with the higher-order post-Newtonian terms are calculated., Comment: 12 pages, 2 figures. Match the published version

The gravitational lensing of gravitational waves might cause beat patterns detectable by interferometers. The feature of this kind of signal is the existence of the beat pattern in the early inspiral phase, followed by a seemingly randomly changing profile. After the strain peaks for the first time, the signal takes the usual waveform and the strain peaks for the second time. Once this signal is detected, the actual magnification factors can be obtained, so the true luminosity distance of the binary system is known. If the lens can be described by a point mass or a singular isothermal sphere, the functional forms of the time delay and the magnification factors are simple enough, so we can infer the mass of the lens or the cosmological parameters., Comment: 9 pages, 4 figures

Similar to the light, gravitational waves traveling in multiple paths may arrive at the same location if there is a gravitational lens on their way. Apart from the magnification of the amplitudes and the time delay between the gravitational wave rays, gravitational lensing also rotates their polarization planes. This results in the changes in the antenna pattern function, which describes the response of the detector to its relative orientation to the gravitational wave. These effects are all reflected in the strain, the signal registered by the interferometers. The gravitational wave rays in various directions stimulate different strains. Their strains differ from each other due to different magnification factors, the phases and the rotation of the polarization plane. The phase difference mainly comes from the time delay. Moreover, the rotation of the polarization plane seemingly introduces the \textit{apparent} vector polarizations, when these strains are compared with each other. Because of the smallness of the deflection angles, the effect of the rotation is negligible., Comment: 6 pages, 1 figure. Match the published version

Gravitational wave emissions (GWEs) of pulsars could not only make them promising targets for continuous gravitational wave searches but also leave imprints in their timing data. We interpret the measured braking index of PSR J1640-4631 with a model involving both the GWE and dipole magnetic field decay. Combining the timing data of PSR J1640-4631 and the theory of magnetic field decay, we propose a new approach of constraining the number of precession cycles, $\xi$, which is highly uncertain currently but can be tightly related to the interior physics of a neutron star and its GWE. We suggest that future observation of the tilt angle $\chi$ of PSR J1640-4631 would not merely help to constrain $\xi$ but also possibly provide information about the internal magnetic field configuration of this pulsar. We find that $\xi$ would be larger than previous estimates unless a tiny angle $\chi\lesssim5^\circ$ is observed. Furthermore, a measured angle $\chi\gtrsim12^\circ$ would indicate $\xi\gtrsim 10^6$, which is at least ten times larger than that suggested previously., Comment: 6 pages, 2 figures, to appear in Phys. Rev. D

Gravitational wave predicted by General Relativity is the transverse wave of spatial strain. Several gravitational waveform signals from binary black holes and from a binary neutron star system accompanied by electromagnetic counterparts have been recorded by advanced LIGO and advanced Virgo. In analogy to light, the spatial fringes of diffraction and interference should also exist as the important features of gravitational waves. We propose that observational detection of such fringes could be achieved through gravitational lensing of continuous gravitational waves. The lenses would play the role of the diffraction barriers. Considering peculiar motions of the observer, the lens and the source, the spatial amplitude variation of diffraction or interference fringes should be detectable as an amplitude modulation of monochromatic gravitational signal., Comment: Accepted for publication in The Astrophysical Journal