The stochastic signal detected by NANOGrav, PPTA, EPTA, and CPTA can be explained by the scalar-induced gravitational waves. In order to determine the scalar-induced gravitational waves model that best fits the stochastic signal, we employ both single- and double-peak parameterizations for the power spectrum of the primordial curvature perturbations, where the single-peak scenarios include the δ-function, box, lognormal, and broken power law model, and the double-peak scenario is described by the double lognormal form. Using Bayesian inference, we find that there is no significant evidence for or against the single-peak scenario over the double-peak model, with log (Bayes factors) among these models ln ℬ < 1. Therefore, we cannot distinguish the different shapes of the power spectrum of the primordial curvature perturbation with the current sensitivity of pulsar timing arrays.

Gravitational-wave astronomy provides a unique new way to study the expansion history of the universe. In this work, we investigate the impact future gravitational-wave observatories will have on cosmology. Third-generation observatories like the Einstein Telescope and Cosmic Explorer will be sensitive to essentially all of the binary black hole coalescence events in the universe. Recent work by Farr et al. points out that features in the stellar-mass black hole population break the mass–redshift degeneracy, facilitating precise determination of the Hubble parameter without electromagnetic counterparts or host galaxy catalogs. Using a hierarchical Bayesian inference model, we show that with one year of observations by the Einstein Telescope, the Hubble constant will be measured to ≲1%. We also show that this method can be used to perform Bayesian model selection between cosmological models. As an illustrative example, we find that a decisive statement can be made comparing the ΛCDM and RHCT cosmological models using two weeks of data from the Einstein Telescope.

Primordial black holes (PBHs) can be not only cold dark matter candidates but also progenitors of binary black holes observed by LIGO-Virgo-KAGRA (LVK) Collaboration. The PBH mass can be shifted to the heavy distribution if multimerger processes occur. In this work, we constrain the merger history of PBH binaries using the gravitational wave events from the third Gravitational-Wave Transient Catalog (GWTC-3). Considering four commonly used PBH mass functions, namely the log-normal, power-law, broken power-law, and critical collapse forms, we find that the multimerger processes make a subdominant contribution to the total merger rate. Therefore, the effect of merger history can be safely ignored when estimating the merger rate of PBH binaries. We also find that GWTC-3 is best fitted by the log-normal form among the four PBH mass functions and confirm that the stellar-mass PBHs cannot dominate cold dark matter.

Recently released data from pulsar timing array (PTA) collaborations provide strong evidence for a stochastic signal consistent with a gravitational-wave background, potentially originating from scalar-induced gravitational waves (SIGWs). However, in order to determine whether the SIGWs with a specific power spectrum of curvature perturbations can account for the PTA signal, one needs to estimate the energy density of the SIGWs, which can be computationally expensive. In this paper, we use a model-independent approach to reconstruct the primordial curvature power spectrum using a free spectrum cross over from 10¹ Mpc^-1 to 10²⁰ Mpc^-1 with NANOGrav 15-year data set. Our results can simplify the task of assessing whether a given primordial curvature power spectrum can adequately explain the observed PTA signal without calculating the energy density of SIGWs.

Recently, the measurements of baryon acoustic oscillations (BAO) by the Dark Energy Spectroscopic Instrument (DESI) indicate a potential deviation from the standard ΛCDM model. Some studies suggest that the data points from the luminous red galaxies (LRG) survey in DESI BAO data may contribute to this discrepancy. In this work, our main goal is to investigate whether this deviation is caused by the parameterization of the equation of state (EoS) of dark energy (DE). Hence, we have examined four popular parameterized dark energy models in our analysis: the Chevallier-Polarski-Linder (CPL), Barboza-Alcaniz (BA), Jassal-Bagla-Padmanabhan (JBP), and Feng-Shen-Li-Li (FSLL) parameterizations. Considering that LRG1 and LRG2 data points may lead to deviation from the ΛCDM model, we use two versions of DESI BAO data, differing in whether these data points are included. Additionally, to break the parameter degeneracies and obtain robust constraint results, we introduce Type Ia supernovae (SNe Ia) and quasars (QSO) in our analysis. Our findings indicate that in these parameterizations, the deviation from (w ₀,w ₁)=(-1,0) becomes more pronounced when using the combined data from DESI BAO, SNe Ia, and QSO compilations. Here, w ₀ and w ₁ represent the EoS of DE. It suggests that the parameterizations of the EoS of DE have little impact on the deviation from the ΛCDM model. Besides, our analysis potentially hints that dark energy may have dynamic properties. In addition, the results obtained from different BAO datasets demonstrate that the LRG1 and LRG2 data points do indeed contribute to a deviation from the ΛCDM model. Finally, according to the statistical criteria, the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), the joint constraints provide substantial observational support to the BA and FSLL models.

Recently, multiple pulsar timing array collaborations have presented compelling evidence for a stochastic signal at nanohertz frequencies, potentially originating from cosmic strings. Cosmic strings are linear topological defects that can arise during phase transitions in the early Universe or as fundamental strings in superstring theory. This paper focuses on investigating the detection capabilities of Taiji, a planned space-based gravitational wave detector, for the gravitational wave background generated by cosmic strings. By analyzing simulated Taiji data and utilizing comprehensive Bayesian parameter estimation techniques, we demonstrate a significant improvement in precision compared to the NANOGrav 15-year data set, surpassing it by an order of magnitude. This highlights the enhanced measurement capabilities of Taiji. Consequently, Taiji can serve as a valuable complementary tool to pulsar timing arrays in validating and exploring the physics of cosmic strings in the early Universe.