arXiv subjects

Zhi-Chao Zhao

Publications and source records attributed to Zhi-Chao Zhao.

At least 19 recordsLinked to original sources

arXiv2026

Optimal all-angle reconstruction of the Hellings-Downs curve

Pulsar timing arrays (PTAs) detect nanohertz gravitational waves through spatial correlations between the timing residuals of different pulsars. For an isotropic, unpolarized stochastic background in general relativity, the ensemble-mean correlation follows the Hellings--Downs (HD) curve; measuring this angular pattern tests the gravitational-wave origin of the signal. Standard bin-by-bin reconstructions optimize the weights within each angular bin separately. We reconstruct the curve jointly using the full pulsar-pair covariance, retaining a free amplitude in every bin. The resulting all-angle best linear unbiased estimator minimizes the variance of every bin value and every linear combination of bins. Applied to the public NANOGrav 15 yr data products, our method reduces the bin standard deviations by up to 12.9\%, with a median reduction of 9.5\%. For a future Square Kilometre Array Observatory (SKAO)-like PTA, the predicted reduction reaches 36.4\%, with a median of 29.6\%, enabling significantly more precise measurements of the gravitational-wave background.

gr-qc↗

arXiv2026

Probing Graviton Mass with MeerKAT PTA and SKA--PTA Forecasts

We present constraints on the graviton mass using the 4.5-year data release from the MeerKAT Pulsar Timing Array (MPTA) and provide forecasts for the upcoming Square Kilometre Array PTA (SKA--PTA). By modeling the modified dispersion relation and the corresponding tensor correlation function for massive gravitons, we perform Bayesian inference on the angular-correlation measurements under three noise configurations (DATA, ER, ALT). Our 90\% credible upper limits on the graviton mass are $m_g < 2.10 \times 10^{-23}\,\mathrm{eV}/c^{2}$ (DATA), $m_g < 2.58 \times 10^{-23}\,\mathrm{eV}/c^{2}$ (ER), and $m_g < 2.25 \times 10^{-23}\,\mathrm{eV}/c^{2}$ (ALT). Including monopolar and dipolar contributions does not significantly alter these bounds, confirming that the constraints are driven by the quadrupolar tensor correlation. All results remain fully consistent with general relativity. For SKA--PTA, we forecast sensitivities down to $m_g \sim 10^{-24}\,\mathrm{eV}/c^{2}$ with a 10-year observing baseline and $m_g \sim 10^{-25}\,\mathrm{eV}/c^{2}$ with a 50-year observing baseline, representing order-of-magnitude improvements over current limits. This work demonstrates the power of current and future PTA observations to test fundamental aspects of gravity in the nanohertz band.

astro-ph.CO↗

arXiv2026

Gravitational lensing of gravitational waves: universal characteristics of strongly lensed memory waveforms

In this work, the strong lensing effect of the memory signal was considered. In the geometric optics limit, the lensed memory signal becomes oscillatory, while the unlensed is basically monotonic. This is because only the high frequency Fourier modes contribute strongly to the lensed signal. Due to the step function like behavior of the unlensed memory waveform, the lensed waveform possesses characteristic morphology that is dependent on the type of the image, but independent of the lens model and the binary system. That is, for each type of the lensed image, the lensed memory waveform has an approximate reflection symmetry about a symmetrical axis in the time domain. More specifically, for the type I and type III images, the lensed memory signals are nearly odd under the reflection, while the type II signal is roughly even. In addition, at the symmetrical axis, the sign of the slope for type I image is different from that for the type III image. These universal characteristic features would help determine the type of the lensed image. This is particularly because the memory waveform can be well approximated by a suitable step function, which involves just two parameters, the overall amplitude and the time of arrival. It is fast and cheap to simulate this approximated waveform. Once the type of the lensed image is determined with the approximated memory waveform, one can use the appropriate waveform template for the oscillatory component of the gravitational wave to perform the parameter estimation.

gr-qc↗

arXiv2026

Solving Hamiltonian Constraint Equation with Physics-Informed Neural Networks

Numerical relativity (NR), solving Einstein equation numerically, plays an important role in source modelling for gravitational wave astronomy. Traditional methods for NR including finite difference method, spectral method and finite element method have been well developed. But newly developed neural network methods for partial differential equations (PDE) have not been well studied yet for NR. We present a Physics-Informed Neural Network (PINN) method to solve the Hamiltonian constraint equation for binary black hole (BBH) initial data in NR. This equation is a highly non-linear elliptic PDE, posing significant challenges for conventional PINN approaches. To overcome these difficulties, we introduce a set of new techniques. We show that our PINN together with these techniques can successfully solve the Hamiltonian constraint equation for generic BBH systems. Validation against the traditional results demonstrates the high accuracy and robustness of our method, revealing the immense potential of constructing a PINN-based initial data solution to all BBH systems for NR.

gr-qc↗

arXiv2026

Constraints on the Sum of Neutrino Masses from ACT DR6 and DESI DR2 Considering Isocurvature Initial Conditions

We present a robust assessment of cosmological constraints on the sum of neutrino masses ($\sum m_ν$) when relaxing the standard assumption of purely adiabatic primordial initial conditions. Allowing for a neutrino density isocurvature (NDI) component alongside the adiabatic mode, we analyse the latest CMB-SPA combination (Planck 2018, ACT DR6, and SPT-3G), DESI DR2 baryon acoustic oscillation data, and the DES Year 5 supernova sample. Within the $Λ$CDM model, the 95\% upper limit weakens only marginally from $\sum m_ν< 0.052$ eV (purely adiabatic) to $< 0.057$ eV (including NDI), with the NDI amplitude consistent with zero. In the CPL dynamical dark energy model, the adiabatic limit is $< 0.111$ eV, shifting to $< 0.115$ eV with NDI, yet the isocurvature mode remains undetected. While these limits are robust against the inclusion of isocurvature perturbations, they are highly sensitive to both the assumed dark energy equation of state and the prior lower bound on $\sum m_ν$. Notably, the adiabatic $Λ$CDM limit of $0.052$ eV lies below the minimum sum required by the normal neutrino mass hierarchy ($0.05878$ eV), indicating that this bound is an artifact of the statistical prior extending to zero. Imposing a physically motivated hierarchy-informed prior raises the limit to $< 0.092$ eV. Our results demonstrate that current data show no evidence for NDI modes and that the inferred neutrino mass upper limit is robust against this extension, but a definitive, model-independent bound requires addressing prior dependencies and dark energy uncertainties. This work provides the first joint constraint on $\sum m_ν$ and NDI using the full CMB-SPA+DESI DR2+DES dataset.

astro-ph.CO↗

arXiv2026

Reassessing the SIGW Interpretation of PTA Signal: The Role of Third-Order Gravitational Waves and Implications for the PBH Overproduction

In light of recent interpretations attributing pulsar timing array (PTA) signal to second-order gravitational waves induced by linear cosmological curvature perturbations in the early universe, the overproduction of primordial black holes (PBHs) poses a theoretical tension. In this work, we address this issue through extending such a scalar-induced gravitational wave (SIGW) framework to include third-order gravitational waves, which allow for a substantial enhancement in the spectral amplitude of SIGWs. Analyzing a combined dataset from cosmic microwave background and baryon acoustic oscillations, we derive cosmological constraints on the physical energy-density fraction of cosmological gravitational waves. Further incorporating PTA data, we obtain constraints on the spectral amplitude and peak frequency of SIGWs. Our results indicate that the parameter region favored by the data combination can to some extent alleviate the PBH overproduction problem, thereby supporting the theoretical consistency of our model. Furthermore, we demonstrate the robustness of our SIGW interpretation for the PTA signal by extending the analysis to include a gravitational wave background from supermassive black hole binaries. These findings are poised for further scrutiny with future high-precision observations.

astro-ph.CO↗

arXiv2026

Forecasting graviton-mass constraints from the full covariance of PTA-astrometry ORF estimators

We develop a full-covariance formalism for pulsar timing array(PTA) -- astrometry verlap reduction function (ORF) estimators and use it to forecast graviton-mass constraints from a nanohertz stochastic gravitational-wave background (SGWB). Analytic covariance expressions are derived for auto- and cross-channel ORF estimators, including signal-signal, noise-noise, and signal-noise contributions, and are validated against numerical simulations. For an observational configuration with sensitivities comparable to NANOGrav and Gaia, we obtain an expected joint 90\% upper limit of $m_g<4.41\times10^{-24}\,\mathrm{eV}/c^2$, which remains PTA-dominated and lies at the same order of magnitude as the existing NANOGrav 15-year PTA-only bound. For a future-like configuration with sensitivities comparable to the SKA and Theia/Gaia-NIR, the astrometric channels contribute significantly to the constraining power, and the joint limit improves to $m_g<0.48 \times 10^{-24} \, \mathrm{eV}/c^2$. These forecasts indicate that PTA -- astrometry multichannel inference provides a viable avenue for improving graviton-mass constraints under next-generation observational conditions.

gr-qc↗

arXiv2026

Exploring the statistical anisotropy of primordial curvature perturbations with pulsar timing arrays

The recent detection of a stochastic gravitational wave background by pulsar timing arrays has opened a new window in understanding supermassive black hole binaries and in probing the universe at the early time. Recently, pulsar timing array (PTA) collaborations have been further paving the way to probe anisotropies in the stochastic gravitational wave background. This study investigates dipole-type statistical anisotropy in the primordial power spectrum within a phenomenological framework. We demonstrate that the primordial dipole induces both dipolar and quadrupolar anisotropies in the energy density spectrum of scalar-induced gravitational waves (SIGWs), without generating extra polarization modes. Based on this anisotropic spectrum, we derive the corresponding PTA overlap reduction functions (ORFs), which exhibit frequency dependence, with the anisotropies enhanced on small scales. Furthermore, owing to the non-uniform distribution of millisecond pulsars over the sky in current PTA dataset, the ORFs exhibit a morphology that explicitly depends on the preferred direction of the anisotropy. However, our bayesian analysis of the NANOGrav 15-year dataset still yields no significant evidence for a preferred direction and a weak upper limit on anisotropy amplitude $(g\lesssim0.5)$. This result arises because the observational frequency band lies below the spectral peak, where our models predict suppressed anisotropic contributions. This limitation highlights the potential of future PTA observations. Specifically, datasets with broader frequency coverage are expected to tighten constraints on dipole-type anisotropy.

gr-qc↗

arXiv2026

Isotropy, anisotropies and non-Gaussianity in the scalar-induced gravitational-wave background: diagrammatic approach for primordial non-Gaussianity up to arbitrary order

Produced nonlinearly by the enhanced linear cosmological curvature perturbations, the scalar-induced gravitational waves (SIGWs) can serve as a potentially powerful probe of primordial non-Gaussianity (PNG) in the early Universe. In this work, we comprehensively investigate the imprints of local-type PNG on the SIGW background beyond the widely used quadratic and cubic approximations. We extend the diagrammatic approach to simplify the calculation of the SIGW energy density spectrum with high-order PNG, thereby facilitating systematic analysis for PNG up to arbitrary order. Following this approach, we derive semi-analytic formulas for the energy-density fraction spectrum, the angular power spectrum, and the angular bispectrum and trispectrum to describe the isotropic component, anisotropies, and non-Gaussianity of the SIGW background, respectively. Particularly, focusing on PNG up to quartic approximation (parameterized by $f_\mathrm{NL}$, $g_\mathrm{NL}$, and $h_\mathrm{NL}$), we numerically compute all contributions to these SIGW spectra. We find that PNG can significantly alter the magnitude of the SIGW energy-density spectrum, and can generate substantial anisotropies through the initial inhomogeneities in the SIGW distribution. Furthermore, we observe that the SIGW angular bispectrum and trispectrum always vanish when the primordial curvature perturbations are Gaussian; otherwise, they do not, indicating their potential utility as probes of PNG. Therefore, we anticipate that the SIGW background will provide essential information about the early Universe.

astro-ph.CO↗

arXiv2025

AInsteinBench: Benchmarking Coding Agents on Scientific Repositories

We introduce AInsteinBench, a large-scale benchmark for evaluating whether large language model (LLM) agents can operate as scientific computing development agents within real research software ecosystems. Unlike existing scientific reasoning benchmarks which focus on conceptual knowledge, or software engineering benchmarks that emphasize generic feature implementation and issue resolving, AInsteinBench evaluates models in end-to-end scientific development settings grounded in production-grade scientific repositories. The benchmark consists of tasks derived from maintainer-authored pull requests across six widely used scientific codebases, spanning quantum chemistry, quantum computing, molecular dynamics, numerical relativity, fluid dynamics, and cheminformatics. All benchmark tasks are carefully curated through multi-stage filtering and expert review to ensure scientific challenge, adequate test coverage, and well-calibrated difficulty. By leveraging evaluation in executable environments, scientifically meaningful failure modes, and test-driven verification, AInsteinBench measures a model's ability to move beyond surface-level code generation toward the core competencies required for computational scientific research.

cs.SE↗

arXiv2025

Constraints on the lepton asymmetry from DESI DR2 BAO data

It is important to explore the potential existence of lepton asymmetry in the neutrino sector. Conducting a joint analysis of DESI DR2 BAO data and \emph{Planck} 2018 CMB data, we obtain the upper limits on the neutrino degeneracy parameter, i.e., $ξ<0.56$ for the normal mass hierarchy while $ξ<0.62$ for the inverted mass hierarchy, at 95\% confidence level. Considering the influence of the dynamical dark energy, we find that these upper limits remain to be robust. This work may provide helpful implications for model buildings of the matter-antimatter asymmetry in the universe.

astro-ph.CO↗

arXiv2025

Study of primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ with the cross-correlations between the scalar-induced gravitational waves and the cosmic microwave background

The stochastic gravitational-wave background originating from cosmic sources contains vital information about the early universe. In this work, we comprehensively study the cross-correlations between the energy-density anisotropies in scalar-induced gravitational waves (SIGWs) and the temperature anisotropies and polarization in the cosmic microwave background (CMB). In our analysis of the angular power spectra for these cross-correlations, we consider all contributions of the local-type primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ that can lead to large anisotropies. We show that the angular power spectra are highly sensitive to primordial non-Gaussianity. Furthermore, we project the sensitivity of future gravitational-wave detectors to detect such signals and, consequently, measure the primordial non-Gaussianity.

astro-ph.CO↗

arXiv2025

New constraints on cosmological gravitational waves from CMB and BAO in light of dynamical dark energy

In this work, we derive upper limits on the physical energy-density fraction today of cosmological gravitational waves, denoted by $Ω_{\rm{gw}}h^{2}$, via analyzing \emph{Planck} \& ACT \& SPT CMB and DESI BAO data combination. In the standard cosmological model, we establish 95\% CL upper limits of $Ω_{\rm{gw}}h^{2} < 1.0 \times 10^{-6}$ for adiabatic initial conditions and $Ω_{\rm{gw}}h^{2} < 2.7 \times 10^{-7}$ for homogeneous initial conditions, assuming a uniform prior for $Ω_{\rm gw}h^{2}$. In light of dynamical dark energy, we get $Ω_{\rm{gw}}h^{2} < 7.2 \times 10^{-7}$ (adiabatic) and $Ω_{\rm{gw}}h^{2} < 2.4 \times 10^{-7}$ (homogeneous). In contrast, if a log-uniform prior was assumed for $Ω_{\rm gw}h^{2}$, these constraints can become tighter by a factor of $\sim4$, suggesting the results to be prior-sensitive. Furthermore, we project the sensitivity achievable with LiteBIRD \& CMB Stage-IV measurements of CMB and CSST observations of BAO, forecasting 68\% CL uncertainties of $σ= 2.5 \times 10^{-7}$ (adiabatic) and $σ= 1.0 \times 10^{-7}$ (homogeneous) for ${Ω_{\rm{gw}}h^{2}}$. The constraints we obtained in this work provide critical benchmarks for exploring the cosmological origins of gravitational waves within the frequency band $f \gtrsim 10^{-15}$\,Hz and potentially enable joint analysis with direct gravitational-wave detection sensitive to this regime.

astro-ph.CO↗

arXiv2025

Space-borne Interferometers to Detect Thousands of Memory Signals Emitted by Stellar-mass Binary Black Holes

The gravitational memory effect manifests gravitational nonlinearity, degenerate vacua, and asymptotic symmetries; its detection is considered challenging. We propose using the space-borne interferometer to detect memory signals from stellar-mass binary black holes (BBHs), typically targeted by ground-based detectors. We use DECIGO detector as an example. Over 5 years, DECIGO is estimated to detect $\sim$2,036 memory signals (SNRs $>$3) from stellar-mass BBHs. Simulations used frequency-domain memory waveforms for direct SNR estimation. Predictions utilized a GWTC-3 constrained BBH population model (Power Law + Peak mass, DEFAULT spin, Madau-Dickinson merger rate). The analysis used conservative lower merger rate limits and considered orbital eccentricity. The high detection rate stems from strong memory signals within DECIGO's bandwidth and the abundance of stellar-mass BBHs. This substantial, conservative detection count enables statistical use of the memory effect for fundamental physics and astrophysics. DECIGO exemplifies that space interferometers may better detect memory signals from smaller mass binaries than their typical targets. Detectors in lower frequency bands are expected to find strong memory signals from $\sim 10^4 M_\odot$ binaries.

gr-qc↗

arXiv2024

Measuring the anisotropies in astrophysical and cosmological gravitational-wave backgrounds with Taiji and LISA networks

We investigate the capabilities of space-based gravitational-wave detector networks, specifically Taiji and LISA, to measure the anisotropies in stochastic gravitational-wave background (SGWB), which are characterized by the angular power spectrum. We find that a detector network can improve the measurement precision of anisotropies by at most fourteen orders of magnitude, depending on the angular multipoles. By doing so, we can enhance our understanding of the physical origins of SGWB, both in astrophysical and cosmological contexts. We assess the prospects of the detector networks for measuring the parameters of angular power spectrum. We further find an inevitable effect of cosmic variance, which can be suppressed by a better angular resolution, strengthening the importance of configuring detector networks. Our findings also suggest a potential detection of the kinematic dipole due to Doppler boosting of SGWB.

gr-qc↗

arXiv2024

Unraveling the early universe's equation of state and primordial black hole production with PTA, BBN, and CMB observations

Pulsar timing array (PTA) data releases showed strong evidence for a stochastic gravitational-wave background in the nanohertz band. When the signal is interpreted by a scenario of scalar-induced gravitational waves (SIGWs), we encounter overproduction of primordial black holes (PBHs). We wonder if varying the equation of state (EoS) of the early Universe can resolve this issue and thereby lead to a consistent interpretation of the PTA data. Analyzing a data combination of PTA, big-bang nucleosynthesis, and cosmic microwave background, we find that an epoch with EoS $w\sim\mathcal{O}(10^{-2})$ between the end of inflation and the onset of radiation domination can significantly suppress the production of PBHs, leading to alleviation of the PBH-overproduction issue. With the inferred interval $w=0.44_{-0.40}^{+0.52}$ at 95\% confidence level, our scenario can interpret the PTA data just as well as the conventional scenario of SIGWs produced during the radiation domination.

astro-ph.CO↗

arXiv2024

Complete analysis of the background and anisotropies of scalar-induced gravitational waves: primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ considered

Investigation of primordial non-Gaussianity holds immense importance in testing the inflation paradigm and shedding light on the physics of the early Universe. In this study, we conduct the complete analysis of scalar-induced gravitational waves (SIGWs) by incorporating the local-type non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$. We develop Feynman-like diagrammatic technique and derive semi-analytic formulas for both the energy-density fraction spectrum and the angular power spectrum. For the energy-density fraction spectrum, we analyze all the relevant Feynman-like diagrams, determining their contributions to the spectrum in an order-by-order fashion. As for the angular power spectrum, our focus lies on the initial inhomogeneities, giving rise to anisotropies in SIGWs, that arise from the coupling between short- and long-wavelength modes due to primordial non-Gaussianity. Our analysis reveals that this spectrum exhibits a typical multipole dependence, characterized by $\tilde{C}_{\ell}\propto[\ell(\ell+1)]^{-1}$, which plays a crucial role in distinguishing between different sources of gravitational waves. Depending on model parameters, significant anisotropies can be achieved. We also show that the degeneracies in model parameters can be broken. The findings of our study underscore the angular power spectrum as a robust probe for investigating primordial non-Gaussianity and the physics of the early Universe. Moreover, our theoretical predictions can be tested using space-borne gravitational-wave detectors and pulsar timing arrays.

astro-ph.CO↗

arXiv2024

Angular bispectrum and trispectrum of scalar-induced gravitational waves: all contributions from primordial non-Gaussianity $f_\mathrm{NL}$ and $g_\mathrm{NL}$

Studying the primordial non-Gaussianity of inflationary perturbations is crucial for testing the inflation paradigm of the early universe. In this work, we conduct a comprehensive analysis of the angular bispectrum and trispectrum of scalar-induced gravitational waves (SIGWs) in the presence of local-type primordial non-Gaussianity parameterized by $f_\mathrm{NL}$ and $g_\mathrm{NL}$, deriving their semi-analytical formulae for the first time. Our findings indicate that it is the presence of primordial non-Gaussianity that leads to a non-Gaussian SIGW background, suggesting that the angular bispectrum and trispectrum of SIGWs could serve as probes of the primordial non-Gaussianity. Our numerical results further illustrate that $f_\mathrm{NL}$ and $g_\mathrm{NL}$ exert significant impacts on the spectral amplitudes, potentially reaching up to $10^{-5}$ for the former and $10^{-8}$ for the latter. In particular, we demonstrate that the angular bispectrum and trispectrum exhibit characteristic dependence on the angular multipoles and frequency bands. They hold potentials to be measured by gravitational-wave detectors that may advance our understanding of the origin of the universe.

astro-ph.CO↗