Search

As a promising dark matter candidate, primordial black holes (PBHs) lighter than $\sim10^{-18}M_{\odot}$ are supposed to have evaporated by today through Hawking radiation. This scenario is challenged by the memory burden effect, which suggests that the evaporation of black holes may slow down significantly after they have emitted about half of their initial mass. We explore the astrophysical implications of the memory burden effect on the PBH abundance by today and the possibility for PBHs lighter than $\sim10^{-18}M_{\odot}$ to persist as dark matter. Our analysis utilizes current LIGO-Virgo-KAGRA data to constrain the primordial power spectrum and infer the PBH abundance. We find a null detection of scalar-induced gravitational waves that accompanied the formation of the PBHs. Then we find that PBHs are ruled out within the mass range $\sim[10^{-24},10^{-19}]M_{\odot}$. Furthermore, we expect that next-generation gravitational wave detectors, such as the Einstein Telescope and the Cosmic Explorer, will provide even more stringent constraints. Our results indicate that future detectors can reach sensitivities that could rule out PBH as dark matter within $\sim[10^{-29}M_{\odot},10^{-16}M_{\odot}]$ in the null detection of scalar-induced gravitational waves., Comment: 9 pages, 2 figures

We parameterize the equation of state of late-time dark energy as $w_{\mathrm{bin}}(z)$, with three redshift bins, characterized by a constant equation of state in each bin. Then, we constrain the parameters of the $w_{\mathrm{bin}}$CDM model using datasets from DESI BAO data, Planck CMB power spectrum, ACT DR6 lensing power spectrum, and type Ia supernova distance-redshift data of Pantheon Plus/DES Y5/Union3. The significances for $w_1>-1$ is $1.9\sigma$, $2.6\sigma$ and $3.3\sigma$, and $w_2$ is consistent with $-1$ within $1\sigma$ level, while $1.6\sigma$, $1.5\sigma$ and $1.5\sigma$ for $w_3<-1$ in these three data combinations with different choices of type Ia supernova datasets, respectively. Additionally, to alleviate $H_0$ tension, we incorporate the early dark energy (EDE) model in the early-time universe and add the SH0ES absolute magnitude $M_b$ prior (or $H_0$ prior) to further constrain the $w_{\mathrm{bin}}$EDE model. In the $w_{\mathrm{bin}}$EDE model, we find a $w_{\mathrm{bin}}(z)$ pattern similar to that in the $w_{\mathrm{bin}}$CDM model. The results of the three data combinations exhibit $w_1>-1$ at $1.9\sigma$, $1.7\sigma$ and $2.9\sigma$ level, meanwhile $w_3<-1$ at $1.3\sigma$, $1.3\sigma$ and $1.3\sigma$ level, respectively. In all, our results indicate that the transition of dark energy from phantom at high redshifts to quintessence at low redshifts is not conclusive., Comment: 10 pages, 4 figures, 2 tables

We propose an analytical approximation for the energy spectrum of the scalar induced gravitational waves (SIGWs) generated by a broken power-law power spectrum, and find that both the asymptotic power-law tails and the intermediate peak contribute distinct features to the SIGW spectrum. Moreover, the broken power-law power spectrum has abundant near-peak features and our results can be used as a near-peak approximation that covers a wide range of models. Our analytical approximation is useful in the rapid generation of the SIGW energy spectrum, which is beneficial for gravitational wave data analysis., Comment: 18 pages, 6 figures, first version

Pulsar timing arrays (PTAs), aimed at detecting gravitational waves (GWs) in the $1\sim 100$ 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., Comment: 18 pages, 6 figures; minor revision and typo corrected

During the fourth observing run of the LIGO-Virgo-KAGRA detector network, the LIGO Livingston observatory detected a coalescing compact binary, GW230529_181500, with component masses of $2.5-4.5\, M_\odot$ and $1.2-2.0\, M_\odot$ at the $90\%$ credible level. The gravitational-wave data alone is insufficient to determine whether the components are neutron stars or black holes. In this paper, we propose that GW230529_181500 originated from the merger of two primordial black holes (PBHs). We estimate a merger rate of $5.0^{+47.0}_{-4.9} \mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ for compact binary coalescences with properties similar to GW230529_181500. Assuming the source is a PBH-PBH merger, GW230529-like events lead to approximately $1.7^{+36.2}_{-1.5} \times 10^{-3}$ of the dark matter in the form of PBHs. The required abundance of PBHs to explain this event is consistent with existing upper limits derived from microlensing, cosmic microwave background observations and the null detection of gravitational wave background by LIGO-Virgo-KAGRA., Comment: 15 pages, 3 figures; Accepted by JCAP

In the recent second part of the third observation run by the LIGO-Virgo-KAGRA collaboration, a candidate with sub-solar mass components was reported, which we labelled as SSM200308. This study investigates the premise that primordial black holes (PBHs), arising from Gaussian perturbation collapses, could explain SSM200308. Through Bayesian analysis, we obtain the primordial curvature power spectrum that leads to the merger rate of PBHs aligning with observational data as long as they constitute {$f_{\mathrm{PBH}}=5.66^{+58.68}_{-5.44}\times 10^{-2}$ } of the dark matter. However, while the gravitational wave (GW) background from binary PBH mergers is within current observational limits, the scalar-induced GWs associated with PBH formation exceed the constraints imposed by pulsar timing arrays, challenging the Gaussian perturbation collapse PBH model as the source of SSM200308., Comment: 9 pages, 3 figures; version accepted for publication in JCAP; typos corrected

Ultralight bosons are attractive dark-matter candidates and appear in various scenarios beyond standard model. They can induce superradiant instabilities around spinning black holes (BHs), extracting the energy and angular momentum from BHs, and then dissipated through monochromatic gravitational radiation, which become promising sources of gravitational wave detectors. In this letter, we focus on massive tensor fields coupled to BHs and compute the stochastic gravitational wave backgrounds emitted by these sources. We then undertake a search for this background within the data from LIGO/Virgo O1$\sim$ O3 runs. Our analysis reveals no discernible evidence of such signals, allowing us to impose stringent limits on the mass range of tensor bosons. Specifically, we exclude the existence of tensor bosons with masses ranging from $4.0\times10^{-14}$ to $2.0\times10^{-12}$ eV at $95\%$ confidence level., Comment: 7 pages, 2 figures

Recently, the emergence of cosmological tension has raised doubts about the consistency of the $\Lambda$CDM model. In order to constrain the neutrino mass within a consistent cosmological framework, we investigate three massive neutrinos with normal hierarchy (NH) and inverted hierarchy (IH) in both the axion-like EDE (Axi-EDE) model and the AdS-EDE model. We use the joint datasets including cosmic microwave background (CMB) power spectrum from Planck 2018, Pantheon of type Ia supernova, baryon acoustic oscillation (BAO) and $H_0$ data from SH0ES. For the $\nu$Axi-EDE model, we obtain $\sum m_{\nu,\mathrm{NH}} < 0.152$ eV and $\sum m_{\nu,\mathrm{IH}} < 0.178$ eV, while for the $\nu$AdS-EDE model, we find $\sum m_{\nu,\mathrm{NH}} < 0.135$ eV and $\sum m_{\nu,\mathrm{IH}} < 0.167$ eV. Our results exhibit a preference for the normal hierarchy in both the $\nu$Axi-EDE model and the $\nu$AdS-EDE model., Comment: 8 pages, 2 figures and 1 table

The recent detection of a stochastic signal in the NANOGrav 15-year data set has aroused great interest in uncovering its origin. However, the evidence for the Hellings-Downs correlations, a key signature of the gravitational-wave background (GWB) predicted by general relativity, remains inconclusive. In this letter, we search for an isotropic non-tensorial GWB, allowed by general metric theories of gravity, in the NANOGrav 15-year data set. Our analysis reveals a Bayes factor of approximately 2.5, comparing the quadrupolar (tensor transverse, TT) correlations to the scalar transverse (ST) correlations, suggesting that the ST correlations provide a comparable explanation for the observed stochastic signal in the NANOGrav data. We obtain the median and the $90\%$ equal-tail amplitudes as $\mathcal{A}_\mathrm{ST} = 7.8^{+5.1}_{-3.5} \times 10^{-15}$ at the frequency of 1/year. Furthermore, we find that the vector longitudinal (VL) and scalar longitudinal (SL) correlations are weakly and strongly disfavoured by data, respectively, yielding upper limits on the amplitudes: $\mathcal{A}_\mathrm{VL}^{95\%} \lesssim 1.7 \times 10^{-15}$ and $\mathcal{A}_\mathrm{SL}^{95\%} \lesssim 7.4 \times 10^{-17}$. Lastly, we fit the NANOGrav data with the general transverse (GT) correlations parameterized by a free parameter $\alpha$. Our analysis yields $\alpha=1.74^{+1.18}_{-1.41}$, thus excluding both the TT ($\alpha=3$) and ST ($\alpha=0$) models at the $90\%$ confidence level., Comment: 9 pages, 4 figures, 3 tables; match the published version

General relativity predicts that gravitational waves propagate at the speed of light. Although ground-based gravitational-wave detectors have successfully constrained the velocity of gravitational waves in the high-frequency range, extending this constraint to the lower frequency range remains a challenge. In this work, we utilize the deviations in the overlap reduction function for a gravitational-wave background within pulsar timing arrays to investigate the velocity of gravitational waves in the nanohertz frequency band. By analyzing the NANOGrav 15-year data set, we obtain a well-constrained lower bound for the velocity of gravitational waves that $v \gtrsim 0.87\,c$, where $c$ is the speed of light., Comment: 6 pages, 1 figure, 1 table

The recently detected stochastic signal by several pulsar timing array collaborations, offers an opportunity to scrutinize the fundamental properties of gravity, including the potential mass of the graviton. In this study, we analyze the NANOGrav 15-year data set to search for a stochastic gravitational wave background with modified Hellings-Downs correlations predicted by massive gravity. While the Bayesian analysis comparing the massive gravity to massless gravity within the effective searchable mass range of $m_g\in [3\times 10^{-25}, 8 \times 10^{-24}]\,\rm{eV}/c^2$ does not yield an explicit upper bound as all the Bayes factors are smaller than $3$, the combined consideration of the minimum frequency inherent in a massive gravity and the observed spectrum leads to an upper limit of $m_g<8.2\times 10^{-24}\,\rm{eV}/c^2$., Comment: 6 pages, 1 figure, 1 table

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, 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., Comment: 24 pages, 5 figures

In the frequency band of Laser Interferometer Space Antenna (LISA), extensive research has been conducted on the impact of foreground confusion noise generated by galactic binaries within the Milky Way galaxy. Additionally, the recent evidence for a stochastic signal, announced by the NANOGrav, EPTA, PPTA, CPTA and InPTA, indicates that the stochastic gravitational-wave background generated by supermassive black hole binaries (SMBHBs) can contribute a strong background noise within in LISA band. Given the presence of such strong noise, it is expected to have a considerable impacts on LISA's scientific missions. In this work, we investigate the impacts of the SGWB generated by SMBHBs on the detection of massive black hole binaries (MBHBs), verified galactic binaries (VGBs) and extreme mass ratio inspirals (EMRIs) in the context of LISA, and find it crucial to resolve and eliminate the exceed noise from the SGWB to ensure the success of LISA's missions., Comment: 6 pages, 3 figures

Primordial black holes (PBHs) are supposed to form through the gravitational collapse of regions with large density fluctuations. The formation of PBHs inevitably leads to the emission of scalar-induced gravitational wave (SIGW) signals, offering a unique opportunity to test the hypothesis of PBHs as a constituent of dark matter (DM). Previous studies have calculated the energy spectrum of SIGWs in local-type non-Gaussian models, primarily considering the contributions from the $F_{\mathrm{NL}}$-order or the $G_{\mathrm{NL}}$-order while neglecting connected diagrams. In this study, we extend the previous work by (i) considering the full contribution of non-Gaussian diagrams up to the $G_{\mathrm{NL}}$-order; (ii) deriving the generic scaling of the SIGW energy spectrum in the infrared region. We derive semi-analytical results applicable to arbitrary primordial power spectra and numerically evaluate the energy spectrum of SIGWs for a log-normal power spectrum., Comment: 21 pages, 2 figures; version accepted for publication in JCAP

The recently released data by pulsar timing array (PTA) collaborations have amassed substantial evidence corroborating the existence of a stochastic signal consistent with a gravitational-wave background at frequencies around the nanohertz regime. We investigate the situation in which the PTA signal originates from scalar-induced gravitational waves~(SIGWs), which serves as a valuable tool to probe the equation of state parameter $w$ during the Universe's early stages. The joint consideration of the PTA data from the NANOGrav 15-year data set, PPTA DR3, and EPTA DR2 yields that $w=0.60^{+0.32}_{-0.39}$ (median + $90\%$ credible interval), indicating a period of condensate domination at the production of SIGWs is allowed by the data. Moreover, the data also supports radiation domination ($w=1/3$) within the $90\%$ credible interval. We also impose an upper bound on the reheating temperature that $T_\mathrm{rh} \lesssim 0.2\,\mathrm{GeV}$ and the constraint on $w$ reveals valuable information on the inflationary potential and the dynamics at the end of inflation., Comment: 19 pages, 3 figures, 1 table; accepted by JCAP

The pulsar timing array (PTA) collaborations have recently reported compelling evidence for the presence of a stochastic signal consistent with a gravitational-wave background. In this letter, we combine the latest data sets from NANOGrav, PPTA and EPTA collaborations to explore the cosmological interpretations for the detected signal from first-order phase transitions, domain walls and cosmic strings, separately. We find that the first-order phase transitions and cosmic strings can give comparable interpretations compared to supermassive black hole binaries (SMBHBs) characterized by a power-law spectrum, but the domain wall model is strongly disfavored with the Bayes factor compared to the SMBHB model being 0.009. Furthermore, the constraints on the parameter spaces indicate that: 1) a strong phase transition at temperatures below the electroweak scale is favored and the bubble collisions make the dominant contribution to the energy density spectrum; 2) the cosmic string tension is $G \mu \in [1.46, 15.3]\times 10^{-12}$ at $90\%$ confidence interval and a small reconnection probability $p<6.68\times 10^{-2}$ is preferred at $95\%$ confidence level, implying that the strings in (super)string theory are strongly favored over the classical field strings., Comment: 10 pages, 5 figures, 2 tables; References updated

The recently released data by pulsar timing array (PTA) collaborations present strong evidence for a stochastic signal consistent with a gravitational-wave background. Assuming this signal originates from scalar-induced gravitational waves, we jointly use the PTA data from the NANOGrav 15-yr data set, PPTA DR3, and EPTA DR2 to probe the small-scale non-Gaussianity. We put the first-ever constraint on the non-Gaussianity parameter, finding $|F_\mathrm{NL}|\lesssim 13.9$ for a lognormal power spectrum of the curvature perturbations. Furthermore, we obtain $-13.9 \lesssim F_\mathrm{NL}\lesssim -0.1$ to prevent excessive production of primordial black holes. Moreover, the multi-band observations with the space-borne gravitational-wave detectors, such as LISA/Taiji/TianQin, will provide a complementary investigation of primordial non-Gaussianity. Our findings pave the way to constrain inflation models with PTA data., Comment: 8 pages, 2 figures, 1 table; Refs added; Supplementary Material added; Accepted by PRD as a Letter

NANOGrav, EPTA, PPTA, and CPTA have announced the evidence for a stochastic signal from their latest data sets. Supermassive black hole binaries (SMBHBs) are supposed to be the most promising gravitational-wave (GW) sources of pulsar timing arrays. Assuming an astro-informed formation model, we use the NANOGrav 15-year data set to constrain the gravitational wave background (GWB) from SMBHBs. Our results prefer a large turn-over eccentricity of the SMBHB orbit when GWs begin to dominate the SMBHBs evolution. Furthermore, the GWB spectrum is extrapolated to the space-borne GW detector frequency band by including inspiral-merge-cutoff phases of SMBHBs and should be detected by LISA, Taiji and TianQin in the near future., Comment: 8 pages, 3 figures, 3 tables; version accepted for publication in SCPMA

Ultralight boson fields, with a mass around $10^{-23}\text{eV}$, are promising candidates for the elusive cosmological dark matter. These fields induce a periodic oscillation of the spacetime metric in the nanohertz frequency band, which is detectable by pulsar timing arrays. In this paper, we investigate the gravitational effect of ultralight tensor dark matter on the arrival time of radio pulses from pulsars. We find that the pulsar timing signal caused by tensor dark matter exhibits a different angular dependence than that by scalar and vector dark matter, making it possible to distinguish the ultralight dark matter signal with different spins. Combining the gravitational effect and the coupling effect of ultralight tensor dark matter with standard model matter provides a complementary way to constrain the coupling parameter $\alpha$. We estimate $\alpha \lesssim 10^{-6}\sim 10^{-5}$ in the mass range $m<5\times 10^{-23}\mathrm{eV}$ with current pulsar timing array., Comment: 13 pages, 3 figures; match the published version

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

Gravitational waves offer a new window to probe the nature of gravity, including answering if the mediating particle, graviton, has a non-zero mass or not. Pulsar timing arrays measure stochastic gravitational wave background (SGWB) at $\sim1-100$~nanohertz. Recently, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration reported an uncorrelated common-spectrum process in their 12.5-year data set with no substantial evidence that the process comes from the SGWB predicted by general relativity. In this work, we explore the possibility of an SGWB from massive gravity in the data set and find that a massless graviton is preferred because of the relatively larger Bayes factor. Without statistically significant evidence for dispersion-related correlations predicted by massive gravity, we place upper limits on the amplitude of the SGWB for graviton mass smaller than $10^{-23}$~eV as $A_{\rm{MG}}<3.21\times 10^{-15}$ at $95\%$ confidence level., Comment: 7 pages, 2 figures, 1 table; accepted for publication in Phys. Rev. D

Both ultralight dark matter and exploring the quantum nature of black holes are all topics of great interest in gravitational wave astronomy at present. The superradiant instability allows an exotic compact object (ECO) to be surrounded by an ultralight boson cloud, which leads to the emission of gravitational waves and further triggers rich dynamical effects. In this paper, we study the gravitational effects of superradiant instabilities by calculating the energy fluxes of gravitational waves emitted from ultralight scalar dark matter fields by solving the Teukolsky equation in the background of a massive ECO phenomenologically described by a Kerr geometry with a reflective boundary condition at its physical boundary. We find that both the amplitude and phase of the reflectivity will either suppress or enhance the energy flux of GWs by several orders of magnitude if $M\mu \gtrsim 0.5$ where $M$ and $\mu$ are the mass of ECO and boson, respectively. However, the modifications to energy flux are negligible if $M \mu \lesssim 0.5$. Our results suggest that reflectivity will play a significant role in the near-horizon physics of ECO., Comment: 20 pages, 6 figures

In this paper, we propose a model in which a spectator field non-minimally couples to an inflaton field and the power spectrum of the perturbation of the spectator field at small scales is dramatically enhanced by the sharp feature in the form of non-minimal coupling. At or after the end of inflation, the perturbation of the spectator field is converted into curvature perturbation and leads to the formation of primordial black holes (PBHs). Furthermore, for example, we consider three phenomenological models for generating PBHs with mass function peaked at $\sim10^{-12}M_\odot$ and representing all the cold dark matter in our Universe and find that the scalar induced gravitational waves generated by the curvature perturbation can be detected by the future space-borne gravitational-wave detectors such as Taiji, TianQin and LISA., Comment: 15 pages and 4 figures; clarifications and refs added

Parity violation is expected to generate an asymmetry between the amplitude of left and right-handed gravitational-wave modes which leads to a circularly polarized stochastic gravitational-wave background (SGWB). Due to the three independent baselines in the LIGO-Virgo network, we focus on the amplitude difference in strain power characterized by Stokes' parameters and do maximum-likelihood estimation to constrain the polarization degree of SGWB. Our results indicate that there is no evidence for the circularly polarized SGWB in the data. Furthermore, by modeling the SGWB as a power-law spectrum, we place upper limit on the normalized energy density $\Omega_\text{gw}(25\,\text{Hz})<5.3\times10^{-9}$ at $95\%$ confidence level after marginalizing over the polarization degree and spectral index., Comment: 6 pages, 4 figures and 2 tables; some clarifications added, version accepted for publication in JCAP

Composed of ultralight bosons, fuzzy dark matter provides an intriguing solution to challenges that the standard cold dark matter model encounters on sub-galactic scales. The ultralight dark matter with mass $m\sim10^{-23} \rm{eV}$ will induce a periodic oscillation in gravitational potentials with a frequency in the nanohertz band, leading to observable effects in the arrival times of radio pulses from pulsars. Unlike scalar dark matter, pulsar timing signals induced by the vector dark matter are dependent on the oscillation direction of the vector fields. In this work, we search for ultralight vector dark matter in the mass range of $[2\times 10^{-24}, 2\times 10^{-22}]{\rm{eV}}$ through its gravitational effect in the Parkes Pulsar Timing Array (PPTA) second data release. Since no statistically significant detection is made, we place $95\%$ upper limits on the local dark matter density as $\rho_{\rm{\tiny{VF}}} \lesssim 5{\rm{GeV/cm^{3}}}$ for $m\lesssim 10^{-23}{\rm{eV}}$. As no preferred direction is found for the vector dark matter, these constraints are comparable to those given by the scalar dark matter search with an earlier 12-year data set of PPTA., Comment: 9 pages, 3 figures, 2 tables; accepted for publication as a Letter in Phys. Rev. D

We put constraints on the normalized energy density in gravitaional waves from cosmic domain walls (DWs) by searching for the stochastic gravitational-wave background (SGWB) in the data of Advanced LIGO and Virgo's first three observing runs. By adopting a phenomenological broken power-law model, we obtain the upper limit of normalized energy density of SGWB generated by DWs in the peak frequency band $10\sim200$ Hz, and get the most stringent limitation at the peak frequency $f_*=35$ Hz, namely $\Omega_\text{DW}(f_*=35\,\text{Hz})<1.4\times10^{-8}$ at $95\%$ confidence level (CL). Subsequently, we work out the constraints on the parameter space in the appealing realization of DW structure -- the heavy axion model which can avoid the so-called quality problem., Comment: 7 pages, 2 tables and 4 figures

As one of the promising candidates of cold dark matter (DM), primordial black holes (PBHs) were formed due to the collapse of over-densed regions generated by the enhanced curvature perturbations during the radiation-dominated era. The enhanced curvature perturbations are expected to be non-Gaussian in some relevant inflation models and hence the higher-order loop corrections to the curvature power spectrum might be non-negligible as well as altering the abundance of PBHs. In this paper, we calculate the one-loop correction to the curvature power spectrum with local-type non-Gaussianities characterizing by $F_{\mathrm{NL}}$ and $G_{\mathrm{NL}}$ standing for the quadratic and cubic non-Gaussian parameters, respectively. Requiring that the one-loop correction be subdominant, we find a perturbativity condition, namely $|2cAF_{\mathrm{NL}}^2+6AG_{\mathrm{NL}}|\ll 1$, where $c$ is a constant coefficient which can be explicitly calculated in the given model and $A$ denotes the variance of Gaussian part of enhanced curvature perturbation, and such a perturbativity condition can provide a stringent constraint on the relevant inflation models for the formation of PBHs., Comment: 6 pages, 5 figures

Gravitational waves (GWs) from compact binary coalescences provide an independent probe of the cosmic expansion history other than electromagnetic waves. In this work, we assume the binary black holes (BBHs) detected by LIGO-Virgo-KAGRA (LVK) collaborations are of primordial origin and constrain the population parameters of primordial black holes (PBHs) and Hubble parameter $H(z)$ using $42$ BBHs from third LVK GW transient catalog (GWTC-3). Three PBH mass models are considered: lognormal, power-law, and critical collapse PBH mass functions. By performing a hierarchical Bayesian population analysis, the Bayes factor strongly disfavors the power-law PBH mass function against the other two in GWTC-3. The constraints on standard $\Lambda{\rm CDM}$ cosmological parameters are rather weak and in agreement with current results. When combining the multi-messenger standard siren measurement from GW170817, the Hubble constant $H_0$ is constrained to be $69^{+19}_{-8}\, \mathrm{km}\, \mathrm{s}^{-1}\, \mathrm{Mpc}^{-1}$ and $70^{+26}_{-8}\, \mathrm{km}\, \mathrm{s}^{-1}\, \mathrm{Mpc}^{-1}$ at $68\%$ confidence for the lognormal and critical collapse mass models, respectively. Furthermore, we consider a mixed ABH+PBH model, in which we assume LVK BBHs can come from both the astrophysical black hole (ABH) and PBH channels. We find that the ABH+PBH model can better describe the mass distribution in GWTC-3 than any single ABH or PBH model, thus improving the precision to constrain the Hubble constant. With the increased BBH events, the mixed ABH+PBH model provides a robust statistical inference for both the population and cosmological parameters., Comment: 10 pages, 6 figures, Accepted for publication in JCAP

We perform a direct search for an isotropic stochastic gravitational-wave background (SGWB) produced by cosmic strings in the Parkes Pulsar Timing Array second data release. We find no evidence for such an SGWB, and therefore place $95\%$ confidence level upper limits on the cosmic string tension, $G\mu$, as a function of the reconnection probability, $p$, which can be less than 1 in the string-theory-inspired models. The upper bound on the cosmic string tension is $G\mu \lesssim 5.1 \times 10^{-10}$ for $p = 1$, which is about five orders of magnitude tighter than the bound derived from the null search of individual gravitational wave burst from cosmic string cusps in the PPTA DR2., Comment: 7 pages, 2 figures, 1 table

Ultralight bosons are promising dark matter candidates and can trigger superradiant instabilities of spinning black holes (BHs), resulting in long-lived rotating "bosonic clouds" around the BHs and dissipating their energy through the emission of monochromatic gravitational waves (GWs). We focus on the scalar bosons minimally coupled with both isolated stellar-origin BHs (SBH) and their binary merger remnants, and perform Bayesian data analysis to search for the stochastic GW background from all the unstable modes that can trigger the superradiant instabilities using the data of Advanced LIGO and Advanced Virgo's first three observing runs. We find no evidence for such signal, and hence rule out the scalar bosons within the mass range $[1.5, 16]\times10^{-13}$ eV, $[1.9, 8.3]\times10^{-13}$ eV and $[1.3, 17]\times10^{-13}$ eV at $95\%$ confidence level for isolated SBHs having a uniform dimensionless spin distribution in $[0,1]$, $[0,0.5]$ and $[0.5,1]$, respectively., Comment: 5 pages, 2 figures and 1 figure; more discussion added, version accepted for publication in PRD

We search for a first-order phase transition (PT) gravitational wave (GW) signal from Advanced LIGO and Advanced Virgo's first three observing runs. Due to the large theoretical uncertainties, four GW energy spectral shapes from bubble and sound wave collisions widely adopted in literature are investigated, separately. Our results indicate that there is no evidence for the existence of such GW signals, and therefore we give the upper limits on the amplitude of GW energy spectrum $\Omega_\text{pt}(f_*)$ in the peak frequency range of $f_*\in [5,500]$ Hz for these four theoretical models, separately. We find that $\Omega_\text{pt}(f_*\simeq 40\ \text{Hz})<1.3\times10^{-8}$ at $95\%$ credible level, and roughly $H_*/\beta\lesssim 0.1$ and $\alpha\lesssim 1$ at $68\%$ credible level in the peak frequency range of $20\lesssim f_*\lesssim 100$ Hz corresponding to the most sensitive frequency band of Advanced LIGO and Advanced Virgo's first three observing runs, where $H_*$ is the Hubble parameter when PT happens, $\beta$ is the bubble nucleation rate and $\alpha$ is the ratio of vacuum and relativistic energy density., Comment: 7 pages, 3 figures, 3 tables; minor revision, some errors corrected

Ultralight bosons, as important candidates of dark matter, can condense around spinning black holes (BHs) to form long-lived ``boson clouds'' due to superradiance instability. The boson-BH system can be observed through gravitational wave detection and may become a new window to find traces of ultralight bosons. In this letter we explore the effects on the superradiant instability of BHs from the near-horizon microstructure. By introducing the reflection parameter near a BH horizon, we derived analytical results on the corrections to both energy levels of bosonic cloud and its characteristic frequencies of superradiance instability. Our results imply that the evolution of a boson-BH system and gravitational waves it emits would be influenced by the near-horizon physics of a BH., Comment: 5 pages

We search for isotropic stochastic gravitational-wave background (SGWB) in the International Pulsar Timing Array second data release. By modeling the SGWB as a power-law, we find very strong Bayesian evidence for a common-spectrum process, and further this process has scalar transverse (ST) correlations allowed in general metric theory of gravity as the Bayes factor in favor of the ST-correlated process versus the spatially uncorrelated common-spectrum process is $30\pm 2$. The median and the $90\%$ equal-tail amplitudes of ST mode are $\mathcal{A}_{\mathrm{ST}}= 1.29^{+0.51}_{-0.44} \times 10^{-15}$, or equivalently the energy density parameter per logarithm frequency is $\Omega_{\mathrm{GW}}^{\mathrm{ST}} = 2.31^{+2.19}_{-1.30} \times 10^{-9}$, at frequency of 1/year. However, we do not find any statistically significant evidence for the tensor transverse (TT) mode and then place the $95\%$ upper limits as $\mathcal{A}_{\mathrm{TT}}< 3.95 \times 10^{-15}$, or equivalently $\Omega_{\mathrm{GW}}^{\mathrm{TT}}< 2.16 \times 10^{-9}$, at frequency of 1/year., Comment: 7 pages, 4 figures, 3 tables

Adopting a binned method, we model-independently reconstruct the mass function of primordial black holes (PBHs) from GWTC-3 and find that such a PBH mass function can be explained by a broad red-tilted power spectrum of curvature perturbations. Even though GW190521 with component masses in upper mass gap $(m>65M_\odot)$ can be naturally interpreted in the PBH scenario, the events (including GW190814, GW190425, GW200105, and GW200115) with component masses in the light mass range $(m<3M_\odot)$ are quite unlikely to be explained by binary PBHs although there are no electromagnetic counterparts because the corresponding PBH merger rates are much smaller than those given by LIGO-Virgo. Furthermore, we predict that both the gravitational-wave (GW) background generated by the binary PBHs and the scalar-induced GWs accompanying the formation of PBHs should be detected by the ground-based and space-borne GW detectors and pulsar timing arrays in the future., Comment: 7 pages, 2 figures; updated to GWTC-3

We search for the isotropic stochastic gravitational-wave background, including the nontensorial polarizations that are allowed in general metric theories of gravity, in the Parkes Pulsar Timing Array (PPTA) second data release (DR2). We find no statistically significant evidence that the common-spectrum process reported by the PPTA collaboration has the tensor transverse, scalar transverse, vector longitudinal, or scalar longitudinal correlations in PPTA DR2. Therefore, we place a $95\%$ upper limit on the amplitude of each polarization mode, as $\mathcal{A}_{\mathrm{TT}} \lesssim 3.2\times 10^{-15}$, $\mathcal{A}_{\mathrm{ST}} \lesssim 1.8\times 10^{-15}$, $\mathcal{A}_{\mathrm{VL}}\lesssim 3.5\times 10^{-16}$ and $\mathcal{A}_{\mathrm{SL}}\lesssim 4.2\times 10^{-17}$; or, equivalently, a $95\%$ upper limit on the energy density parameter per logarithm frequency, as $\Omega_{\mathrm{GW}}^{\mathrm{TT}} \lesssim 1.4\times 10^{-8}$, $\Omega_{\mathrm{GW}}^{\mathrm{ST}} \lesssim 4.5\times 10^{-9}$, $\Omega_{\mathrm{GW}}^{\mathrm{VL}} \lesssim 1.7\times 10^{-10}$ and $\Omega_{\mathrm{GW}}^{\mathrm{SL}} \lesssim 2.4\times 10^{-12}$, at a frequency of 1/yr., Comment: 7 pages, 2 figures, and 4 tables; ApJ in press

In this letter we calculate the gravitational waves (GWs) emitted from a small binary (SB) by solving the Teukolsky equation in the background of a massive exotic compact object (ECO) which is phenomenologically described by a Schwarzschild geometry with a reflective boundary condition at its "would-be" horizon. The "continuous echo" waves propagating to infinity due to reflectivity of ECO at its "would-be" horizon provide an exquisite probe to the nature of the ECO's horizon., Comment: 6 pages, 3 figures; Detectability of the continuous echo added

We investigate how the production of gravitational waves (GWs) is affected by the GW velocity $(c_T)$ during preheating after inflation. For instance, we simulate the production of GWs after $\lambda\phi^4$ chaotic inflation, and find that GW spectrum is enhanced for $c_T<1$, but distorted (suppressed at low frequency, but enhanced at high frequency) for $c_T>1$., Comment: 5 pages and 2 figures

We perform the first search for an isotropic non-tensorial gravitational-wave background (GWB) allowed in general metric theories of gravity in the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 12.5-year data set. By modeling the GWB as a power-law spectrum, we find strong Bayesian indication for a spatially correlated process with scalar transverse (ST) correlations whose Bayes factor versus the spatially uncorrelated common-spectrum process is $107\pm 7$, but no statistically significant evidence for the tensor transverse, vector longitudinal and scalar longitudinal polarization modes. The median and the $90\%$ equal-tail amplitudes of ST mode are $\mathcal{A}_{\mathrm{ST}}= 1.06^{+0.35}_{-0.28} \times 10^{-15}$, or equivalently the energy density parameter per logarithm frequency is $\Omega_{\mathrm{GW}}^{\mathrm{ST}} = 1.54^{+1.21}_{-0.71} \times 10^{-9}$, at frequency of 1/year., Comment: 6 pages, 2 tables and 2 figures; version under review which was revised before arXiv:2109.14706

Oscillons are long-lived, localized, oscillating nonlinear excitations of a real scalar field which can be abundantly produced during preheating after inflation. We give the first $(3+1)$-dimensional simulation for the oscillon formation during preheating with noncanonical kinetic terms, e.g. the Dirac-Born-Infeld form, and find that the formation of oscillons is significantly influenced by the noncanonical effect., Comment: 5 pages, 4 figures; more results added, version accepted for publication in PLB

The current observational constraints still leave a substantial mass window $\sim [10^{-16},10^{-14}] \cup [10^{-13},10^{-12}] M_\odot$ for primordial black holes (PBHs) representing all of dark matter (DM) in our Universe. The gravitational waves (GWs) induced by the curvature perturbations are inevitably generated during the formation of these PBHs, and fall in the frequency band of LISA. Such scalar induced gravitational waves (SIGWs) are supposed to be definitely detected by LISA even when the second-order local-type non-Gaussianity characterized by the parameter $F_{\rm NL}$ is taken into account. In this letter, we give a comprehensive analysis of the GWs induced by the local-type non-Gaussian curvature perturbations up to the third-order denoted by the non-linear parameter $G_{\rm NL}$, and find that a log-dependent slope of SIGWs in the infrared region is generically predicted and the amplitude of SIGWs can be further suppressed by several orders of magnitude. Therefore, the null-detection of SIGWs by LISA cannot rule out the possibility of PBHs making up all of DM., Comment: 6 pages, 3 figures; version accepted for publication

We measure the expansion rate of the recent Universe and the calibration scale of the baryon acoustic oscillation (BAO) from low-redshift data. BAO relies on the calibration scale, i.e., the sound horizon at the end of drag epoch $r_d$, which often imposes a prior of the cosmic microwave background (CMB) measurement from the Planck satellite. In order to make really independent measurements of $H_0$, we leave $r_d$ completely free and use the BAO data sets combined with the 31 observational $H(z)$ data, GW170817 and Pantheon sample of Type Ia supernovae. In $\Lambda$CDM model, we get $H_0=68.63^{+1.75}_{-1.77}$ km s$^{-1}$ Mpc$^{-1}$, $r_d=146.85^{+3.29}_{-3.77}$ Mpc. For the two model-independent reconstructions of $H(z)$, we obtain $H_0=68.02\pm1.82$ km s$^{-1}$ Mpc$^{-1}$, $r_d=148.18^{+3.36}_{-3.78}$ Mpc in the cubic expansion, and $H_0=68.58\pm1.76$ km s$^{-1}$ Mpc$^{-1}$, $r_d=148.02^{+3.63}_{-3.60}$ Mpc in the polynomial expansion. The values of Hubble constant $H_0$ and sound horizon $r_d$ are consistent with the estimate derived from the Planck CMB data assuming a flat $\Lambda$CDM model, but $H_0$ is in $2.4\sim2.6$ $\sigma$ tension with SH0ES 2019, respectively., Comment: 8 pages, 5 figures, 3 tables

Cosmic Microwave Background (CMB) anisotropy encodes a lot of information about our Universe. In this paper we take the ground-based CMB observations (GCMB), including the South Pole Telescope (SPT), SPTpol and the Atacama Cosmology Telescope Polarimeter (ACTPol), as a new probe to the CMB anisotropy independent of two satellite observations, i.e. Wilkinson Microwave Anisotropy Probe (WMAP) and Planck. The combination of current GCMB data is consistent with WMAP and Planck. In the spatially flat $\Lambda$CDM model, the Hubble constant is $H_0=69.72\pm 1.63$ km/s/Mpc at $68\%$ confidence level (CL). Combining with baryon acoustic oscillation (BAO) and the Pantheon sample of Type Ia supernovae (SN), we find that $H_0=68.40\pm 0.58$ km/s/Mpc ($68\%$ CL) in the spatially flat $\Lambda$CDM cosmology which has a tension with local measurement given by Riess et al. in 2019 at $3.7\sigma$ level, and $\Omega_k=-0.0013\pm 0.0039$ and $N_{\rm{eff}}=2.90\pm 0.41$ ($68\%$ CL) in the extended cosmological models., Comment: 7 pages and 6 figures

In this letter we calculate the scalar induced gravitational waves (SIGWs) accompanying the formation of primordial black hole during the radiation dominated era in three different gauges, i.e. synchronous gauge, Newton gauge and uniform curvature gauge, and we find that the energy density spectra of SIGWs, $\ogw(k)$, are identical in these three different gauges., Comment: 2 figures, 8 pages; errors in I(u,v) corrected; version accepted for publication

Adopting the low-redshift observational datasets, including the Pantheon sample of Type Ia supernovae, baryon acoustic oscillation measurements, and the tomographic Alcock-Paczynski method, we determine the Hubble constant to be $67.95^{+0.78}_{-1.03}$ , $69.81^{+2.22}_{-2.70}$ and $66.75^{+3.42}_{-4.23}$ km s$^{-1}$ Mpc$^{-1}$ at 68\% confidence level in the $\Lambda$CDM, $w$CDM and $w_0w_a$CDM models, respectively. Compared to the Hubble constant given by Riess et al. in 2019, we conclude that the new physics beyond the standard $\Lambda$CDM model is needed if all of these datasets are reliable., Comment: 4 pages, 1 figure

The detection of binary black hole coalescences by LIGO/Virgo has aroused the interest in primordial black holes (PBHs), because they could be both the progenitors of these black holes and a compelling candidate of dark matter (DM). PBHs are formed soon after the enhanced scalar perturbations re-enter horizon during radiation dominated era, which would inevitably induce gravitational waves as well. Searching for such scalar induced gravitational waves (SIGWs) provides an elegant way to probe PBHs. We perform the first direct search for the signals of SIGWs accompanying the formation of PBHs in North American Nanohertz Observatory for Gravitational waves (NANOGrav) 11-year data set. No statistically significant detection has been made, and hence we place a stringent upper limit on the abundance of PBHs at $95\%$ confidence level. In particular, less than one part in a million of the total DM mass could come from PBHs in the mass range of $[2 \times 10^{-3}, 7\times 10^{-1}] \Msun$., Comment: 7 pages, 2 table, 2 figures; Typos and errors corrected; replaced by refined figures; version accepted for publication in PRL

We analytically calculate the scalar induced gravitational waves (SIGWs) and find a log-dependent slope of SIGW in the infrared regions $(f

Assuming that primordial black holes compose a fraction of dark matter, some of them may accumulate at the center of galaxy and perform a prograde or retrograde orbit against the gravity pointing towards the center exerted by the central massive black hole. If the mass of primordial black holes is of the order of stellar mass or smaller, such extreme mass ratio inspirals can emit gravitational waves and form a background due to incoherent superposition of all the contributions of the Universe. We investigate the stochastic gravitational-wave background energy density spectra from the directional source, the primordial black holes surrounding Sagittarius A$^\ast$ of the Milky Way, and the isotropic extragalactic total contribution, respectively. As will be shown, the resultant stochastic gravitational-wave background energy density shows different spectrum features such as the peak positions in the frequency domain for the above two kinds of sources. Detection of stochastic gravitational-wave background with such a feature may provide evidence for the existence of primordial black holes. Conversely, a null searching result can put constraints on the abundance of primordial black holes in dark matter., Comment: 10 pages, 7 figures. Published version in Physical Review D

Primordial gravitational waves generated during inflation lead to the B-mode polarization in the cosmic microwave background and a stochastic gravitational wave background in the Universe. We will explore the current constraint on the tilt of primordial gravitational-wave spectrum, and forecast how the future observations can improve the current constraint., Comment: 3 pages, 2 figures

The possibility that primordial black holes (PBHs) represent all of the dark matter (DM) in the Universe and explain the coalescences of binary black holes detected by LIGO/Virgo has attracted a lot of attention. PBHs are generated by the enhancement of scalar perturbations which inevitably produce the induced gravitational waves (GWs). We calculate the induced GWs up to the third-order correction which not only enhances the amplitude of induced GWs, but also extends the cutoff frequency from $2k_*$ to $3k_*$. Such effects of the third-order correction lead to an around $10\%$ increase of the signal-to-noise ratio (SNR) for both LISA and pulsar timing array (PTA) observations, and significantly widen the mass range of PBHs in the stellar mass window accompanying detectable induced GWs for PTA observations including IPTA, FAST and SKA. On the other hand, the null detections of the induced GWs by LISA and PTA experiments will exclude the possibility that all of the DM is comprised of PBHs and the GW events detected by LIGO/Virgo are generated by PBHs., Comment: 6 pages, 2 figures; typos corrected and refs added

We update the constraints on the power spectra of primordial curvature perturbation and tensor perturbation including Planck data 2015 (P15) and recently released BICEP2/Keck data (BK15), Baryon Acoustic Oscillation data and the Type Ia supernovae data. We find that the upper limits of tensor-to-scalar ratio are $0.061$, $0.064$ and $0.072$ at $95\%$ confidence level (CL) in the $\Lambda$CDM+$r$, $\Lambda$CDM+$r$+$\alpha_s$ and $\Lambda$CDM+$r$+$\alpha_s$+$\beta_s$ models respectively, where $\alpha_s$ and $\beta_s$ are the running of scalar spectral index and running of running. The inflation model with a concave potential is favored at more than $95\%$ CL. In addition, parametrizing the slow-roll parameter $\epsilon\sim 1/N^p$, where $N$ is the e-folding number before the end of inflation and taken in the range of $[50,60]$ and $[14,75]$ respectively, we conclude that the inflation model with a monomial potential $V(\phi)\sim \phi^n$ is disfavored at more than $95\%$ CL, and both the Starobinsky inflation model and brane inflation model are still consistent with the data., Comment: 6 pages, 5 figures