arXiv subjects

Lang Liu

Publications and source records attributed to Lang Liu.

At least 19 recordsLinked to original sources

arXiv2026

Alternative LISA-TAIJI networks: polarization separation of the stochastic gravitational wave background

Stochastic gravitational-wave backgrounds (SGWBs) provide a unique opportunity to probe both unresolved astrophysical populations and fundamental physics in the early Universe. Future space-based gravitational-wave (GW) detectors, such as LISA and TAIJI, will enable cross-correlation observations that are particularly sensitive to SGWBs and their polarization content. In this work, we investigate the capabilities of two proposed LISA-TAIJI networks, LISA-TAIJIp and LISA-TAIJIm, for detecting and discriminating tensor, vector, and scalar polarization components of isotropic SGWBs. Using the cross-correlation between the two networks, we evaluate their sensitivities and signal-to-noise ratios for SGWBs containing different combinations of polarization sectors. We find that the LISA-TAIJIm configuration, which has a larger relative inclination between the two constellations, exhibits substantially weaker polarization degeneracies and significantly improved performance in separating polarization components, particularly for tensor-vector-scalar backgrounds. Fisher-matrix forecasts for power-law SGWBs show that the two configurations yield broadly comparable constraints on spectral parameters, reflecting the different roles of component separation and parameter estimation. Our results demonstrate that large-angle LISA-TAIJI networks provide a more favorable geometry for model-independent SGWB polarization measurements.

gr-qc↗

arXiv2026

Scalar-induced gravitational waves from a box-shaped curvature power spectrum

We compute the stochastic background of gravitational waves (GWs) produced at second order in cosmological perturbation theory by a primordial curvature power spectrum that is flat in $\ln k$ over a finite band $[k_-,k_+]=[k_*e^{-\Delta},k_*e^{+\Delta}]$ and vanishes elsewhere. This logarithmic box interpolates between a monochromatic spectrum as $\Delta\to0$ and a locally scale-invariant plateau as $\Delta\to\infty$, and its sharp boundaries make the geometry of the source convolution unusually transparent. Working in the radiation era, we reduce the convolution to a compact integral over the overlap between the momentum triangle and the box, and evaluate it analytically in two regimes. For a narrow box we show that, to leading order in the width, the spectrum equals the Dirac-spectrum result multiplied by a purely geometric overlap factor $\Phi_{\rm box}(\kappa,\Delta)$; this factor turns the infrared slope from $k^{3}\ln^{2}k$ into $k^{2}\ln^{2}k$ at a break $k_b=2k_*\sinh\Delta$. For a broad box we separate the lower edge, the scale-invariant interior, and the upper edge, derive the leading behaviour in each (an infrared $k^{3}\ln^{2}k$ rise, a scale-invariant plateau, and a quartic cut-off at the hard endpoint $k=2k_+$), and combine them into a single uniform formula cast as a product of two universal, $\Delta$-independent edge functions. We also provide an integral-free closed-form surrogate for these edge functions for use in parameter scans.

gr-qc↗

arXiv2025

Inspiraling binary charged black holes in an external magnetic field: Application of post-Newtonian dynamics in Einstein-Maxwell theory

We present a systematic post-Newtonian treatment of binary charged black holes immersed in external magnetic fields within the framework of Einstein-Maxwell theory. By incorporating a uniform external magnetic field into the two-body Lagrangian expanded to first post-Newtonian order, we derive the complete equations of motion that capture both gravitational and electromagnetic interactions. The magnetic Lorentz force fundamentally alters the orbital dynamics, breaking the conservation of linear and angular momentum and inducing transitions from planar to three-dimensional trajectories. {Through numerical integration of these equations, we compute the resulting gravitational waveforms and characterize the distinctive magnetic field signatures through time-domain and frequency-domain analysis.} Our results demonstrate that strong background magnetic fields can substantially modify the orbital evolution and leave distinctive signatures in the gravitational wave signals. These findings provide a promising avenue for detecting charged black holes and probing magnetic field environments through gravitational wave observations.

gr-qc↗

arXiv2025

GW231123 Mass Gap Event and the Primordial Black Hole Scenario

We investigate the possibility that the recently reported GW231123 event, with component masses $M_1=137^{+22}_{-17}\,M_\odot$, $M_2=103^{+20}_{-52}\,M_\odot$ and a local merger rate $R_{\mathrm{local}}=0.08^{+0.19}_{-0.07}\,\mathrm{Gpc^{-3}\,yr^{-1}}$, originates from primordial black holes (PBHs) formed during an early matter-dominated era. We compute the PBH mass function, abundance, spin distribution and the merger rate density and find a set of choices for the parameters to reproduce the key properties of GW231123. While PBHs formed in such a scenario can acquire large spins through sustained tidal torques, the spin distribution remains uncertain and additional accretion might lead to extreme spin values inferred in GW231123. We also show that the resulting PBH abundance, $f_{\mathrm{pbh}}=1.64^{+5.00}_{-1.59}\times10^{-1}$, lies close to the exclusion bounds from CMB accretion limits and other probes, highlighting a potential tension with current constraints. Finally, we estimate the scalar-induced gravitational waves (SIGWs) that are inevitably generated during PBH formation. PBHs that interpret GW231123 are accompanied by negligible SIGWs in the nano-hertz band, indicating no conflict with current pulsar timing arrays data.

astro-ph.CO↗

arXiv2025

Gravitational wave cosmology

Gravitational waves (GWs) originating from cosmological sources offer direct insights into the physics of the primordial Universe, the fundamental nature of gravity, and the cosmic expansion of the Universe. In this review paper, we present a comprehensive overview of our recent advances in GW cosmology, supported by the national key research and development program of China, focusing on cosmological GW sources and their implications for fundamental physics and cosmology. We first discuss the generation mechanisms and characteristics of stochastic gravitational wave backgrounds generated by physical processes occurred in the early Universe, including those from inflation, phase transitions, and topological defects, and summarize current and possible future constraints from pulsar timing array and space-based detectors. Next, we explore the formation and observational prospects of primordial black holes as GW sources and their potential connection to dark matter. We then analyze how GWs are affected by large-scale structure, cosmological perturbations, and possible modifications of gravity on GW propagation, and how these effects can be used to test fundamental symmetry of gravity. Finally, we discuss the application of GW standard sirens in measuring the Hubble constant, the expansion history, and dark energy parameters, including their combination with electromagnetic observations. These topics together show how GW observations, especially with upcoming space-based detectors, such as LISA, Taiji, and Tianqin, can provide new information about the physics of the early Universe, cosmological evolution, and the nature of gravity.

gr-qc↗

arXiv2025

Polynomial Potential Inflation in the ACT Era: From CMB to Primordial Black Holes

The recent measurements from the Atacama Cosmology Telescope (ACT) favor a higher value of the scalar spectral index $n_s$ compared to the Planck data, challenging many well-established inflationary models. In this work, we investigate the viability of polynomial potential inflation in light of the latest ACT data, systematically analyzing cases from $n=2$ to $n=5$. By exploring the parameter space and deriving constraints on the model coefficients, we find that the cubic to quintic models can provide a good fit to the data, while the quadratic model struggles to simultaneously accommodate the ACT data and the requirement of sufficient inflation. Notably, the quintic case ($n=5$) not only matches cosmic microwave background (CMB) observations but also produces an inflection point that simultaneously triggers primordial black hole formation and generates a scalar-induced gravitational wave. These findings establish higher-order polynomial potentials as compelling frameworks and reconcile precision CMB measurements with multi-messenger probes of early-universe physics.

astro-ph.CO↗

arXiv2025

Reconciling Nonminimally Coupled Higgs Inflation with ACT DR6 Observations through Reheating

The Higgs inflation model with nonminimal coupling, while disfavored by the 1$\sigma$ region of the latest Atacama Cosmology Telescope Data Release 6 (ACT DR6) observational data, can be reconciled with the ACT DR6 data by incorporating the effects of reheating. In this paper, we consider reheating with a constant equation of state $w_{re}$. For the strong coupling case $\xi=100$, we find that reconciling the model with both the ACT DR6 constraints and the minimum reheating temperature required for successful Big Bang Nucleosynthesis (BBN) demands $w_{re} \geq 0.92$. Specifically, the reheating $e$-folding number must be $ N_{ re}= 28.3$ for $w_{ re} = 0.92$, and within $24.9 \leq N_{ re} \leq 27.2$ for $w_{ re} = 1$. In the more general case without assuming the strong coupling limit, consistency with both ACT and BBN requires the nonminimal coupling to satisfy $\xi \geq 0.05$. Our findings suggest that by considering reheating, a wide range of inflationary models, such as $R^2$ inflation, hilltop inflation, E-model inflation, and T-model inflation, can also be made consistent with the ACT DR6 observational data.

astro-ph.CO↗

arXiv2025

On the Gauge Invariance of Secondary Gravitational Waves

Second-order tensor perturbations induced by primordial fluctuations play a crucial role in probing small-scale physics, but gauge dependence of their energy density has remained a fundamental challenge in cosmological perturbation theory. We address this issue by introducing a boundary condition-based filtering method that extracts physical radiation through the Sommerfeld criterion. We demonstrate that after filtering non-physical modes, the energy density of secondary gravitational waves becomes gauge-invariant and exhibits physically consistent behavior in the sub-horizon limit. This approach provides a unified framework for both adiabatic and isocurvature perturbations, enhancing theoretical predictions and observational signatures of early universe physics.

astro-ph.CO↗

arXiv2024

Implications for the non-Gaussianity of primordial gravitational waves from pulsar timing arrays

The detection of a stochastic signal by recent pulsar timing array (PTA) collaborations, including NANOGrav, PPTA, EPTA+InPTA, CPTA and MPTA, has opened a new window to explore gravitational waves (GWs) at nanohertz frequencies. Motivated by the possibility that such a signal could arise from primordial gravitational waves (PGWs), we investigate the implications of tensor non-Gaussianity for the PGW power spectrum. Utilizing PTA data sets, we provide constraints on local-type tensor non-Gaussianity parameter ${F}_{\mathrm{NL}}$. We find $|{F}_{\mathrm{NL}}|\lesssim 7.97$ for a log-normal PGW power spectrum. Our analysis reveals that even moderate tensor non-Gaussianity can lead to significant deviations from standard predictions, thereby offering a novel means to test inflationary scenarios and probe the underlying dynamics of the early Universe. Future multi-band GW observatories, such as LISA, Taiji, and TianQin, will be instrumental in complementing these efforts and further refining our understanding of tensor non-Gaussianity.

astro-ph.CO↗

arXiv2024

Constraints on Pre-Big-Bang Cosmology from Advanced LIGO and Advanced Virgo's First Three Observing Runs

We search for the stochastic gravitational-wave background (SGWB) predicted by pre-big-bang (PBB) cosmology using data from the first three observing runs of Advanced LIGO and Advanced Virgo. PBB cosmology proposes an alternative to cosmic inflation where the Universe evolves from a weak-coupling, low-curvature state to the hot Big Bang through a high-curvature bounce phase, predicting a distinctive SGWB spectrum. We perform a Bayesian analysis of the cross-correlation data to constrain the model parameters characterizing the PBB spectrum. We find no evidence for a PBB-induced SGWB, with a Bayes factor of $0.03$ between the PBB and noise-only model, strongly favoring the noise-only hypothesis. Our analysis establishes a lower bound $\beta \gtrsim -0.19$ at $95\%$ confidence level, which is compatible with the theoretical requirement $\beta \geq 0$ for a smooth bounce transition. While we do not detect a signal, our constraints remain consistent with the basic theoretical framework of PBB cosmology, demonstrating the potential of gravitational-wave observations to test early Universe theories.

astro-ph.CO↗

arXiv2024

Pre-Big-Bang Cosmology Cannot Explain NANOGrav 15-year Signal

We investigate whether the Pre-Big Bang (PBB) scenario from string cosmology can explain the stochastic gravitational wave background signal reported in the NANOGrav 15-year dataset. Using Bayesian analysis techniques, we constrain the key parameters of the PBB model by comparing its theoretical predictions with the observed data. Our analysis yields $\beta = -0.12^{+0.06}_{-0.21}$ ($90\%$ credible interval) for the dilaton-dynamics parameter, which lies outside the theoretically allowed range $0 \leq \beta < 3$ with more than $5\sigma$ confidence. Additionally, model comparison strongly favors a simple power-law spectrum over the PBB scenario, with a Bayes factor of approximately $468$. These results demonstrate that the PBB scenario, in its current formulation, cannot adequately explain the NANOGrav observations, highlighting the need for either significant modifications to the model or alternative explanations for the observed signal.

astro-ph.CO↗

arXiv2024

Gauge Dependence of Gravitational Waves Induced by Primordial Isocurvature Fluctuations

Primordial isocurvature perturbations, which can arise from various sources in the early Universe, have the potential to leave observable imprints on the gravitational-wave background and provide insights into the nature of primordial fluctuations. In this study, we investigate the gauge dependence of induced gravitational waves (IGWs) sourced by these isocurvature perturbations during radiation dominated era and the kination period in the early universe. We analyze the energy density spectra of IGWs in three different gauges: synchronous, Newtonian, and uniform curvature gauges. To facilitate this analysis, we derive analytical solutions for the perturbations that contribute to the IGW spectra and a general gauge transformation from Newtonian gauge to an arbitrary gauge. Our results reveal significant differences in the energy spectra across these gauges. We find that the energy density of IGWs during radiation domination increases with conformal time as $\eta^8$ and $\eta^4$ for synchronous and uniform curvature gauges, respectively, while it converges in the Newtonian gauge. These findings highlight the importance of gauge choice in calculating IGWs and have implications for the interpretation of future observations of the gravitational-wave background.

gr-qc↗

arXiv2024

Constraining string cosmology with the gravitational-wave background using the NANOGrav 15-year data set

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 $\Omega_\mathrm{gw}^{s}$ 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 $f_s = 1.2^{+0.6}_{-0.6}\times 10^{-8} \mathrm{Hz}$ and $\Omega_\mathrm{gw}^{s} = 2.9^{+5.4}_{-2.3}\times 10^{-8}$, 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.

gr-qc↗

arXiv2024

Search for a Gravitational-Wave Background from Sound Speed Resonance from Advanced LIGO and Advanced Virgo's First Three Observing Runs

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 $|\tau_0| \lesssim 5.9 \times 10^3\,\mathrm{s}$ 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.

astro-ph.CO↗

arXiv2024

The Benefits of Balance: From Information Projections to Variance Reduction

Data balancing across multiple modalities and sources appears in various forms in foundation models in machine learning and AI, e.g. in CLIP and DINO. We show that data balancing across modalities and sources actually offers an unsuspected benefit: variance reduction. We present a non-asymptotic statistical bound that quantifies this variance reduction effect and relates it to the eigenvalue decay of Markov operators. Furthermore, we describe how various forms of data balancing in contrastive multimodal learning and self-supervised clustering can be better understood, and even improved upon, owing to our variance reduction viewpoint.

stat.ML↗

arXiv2024

Pairing phase transition in the odd-A nuclei: identification and classification

The investigation into the pairing phase transition in the odd-A nucleus 161Dy utilizes a sophisticated blend of covariant density functional theory and the shell-model-like approach. It is discerned that variations in thermodynamic quantities at the critical temperature do not exclusively align with pairing phase transitions. The presence of an S-shaped heat capacity curve, often interpreted as an indication of such transitions, does not offer a definitive confirmation. Additional factors, including the blocking effect, can modify the heat capacity curve and impede the transition process. The pairing phase transition in 161Dy, occurring around 0.7 to 1.0 MeV, is unequivocally characterized as a first-order transition. Furthermore, an exploration into the impact of varying strengths of pairing correlations on these transitions reveals a nonlinear relationship, adding complexity to the transition dynamics.

nucl-th↗

arXiv2024

Constraining the nonstandard propagating gravitational waves in the cosmological background with GWTC-3

The detection of gravitational waves (GWs) has opened a new window to test the fundamental nature of gravity. We present constraints on the nonstandard propagation of GWs using the spectral siren method applied to binary black hole (BBH) mergers from the third Gravitational-Wave Transient Catalog (GWTC-3). The spectral siren method exploits the redshift distribution of BBHs to probe the cosmic expansion history and break degeneracies between cosmology and modified gravity effects. We focus on the friction term $\nu$ in the nonstandard GW propagation equation, which characterizes the running of the Planck mass. Assuming the standard $\Lambda$CDM cosmology, we find $\nu = 0.5^{+3.5}_{-2.6}$ (median and $90\%$ credible interval), improving upon previous constraints from the bright siren event GW170817 by an order of magnitude. This improvement is due to the higher redshifts of BBHs in GWTC-3, reaching up to $z \sim 1$. Our result suggests that the propagation of GWs is consistent with the predictions of general relativity, placing limits on modified gravity theories that predict a time-varying Planck mass. As the sensitivity of GW detectors improves, the spectral siren method will provide a powerful tool for testing gravity on cosmological scales and probing the physics of the early Universe.

astro-ph.CO↗

arXiv2024

Detecting a Gravitational-Wave Background from Inflation with Null Energy Condition Violation: Prospects for Taiji

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.

gr-qc↗