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 furthe
r 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 $30pm 2$. 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.
Adopting a binned method, we model-independently reconstruct the mass function of primordial black holes (PBHs) from GWTC-2 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.
We search for isotropic stochastic gravitational-wave background including non-tensorial polarizations allowed in general metric theories of gravity in the Parkes Pulsar Timing Array (PPTA) second data release (DR2). We find no statistically signific
ant evidence that the common process reported by the PPTA collaboration has the tensor transverse (TT), scalar transverse (ST), vector longitudinal (VL), or scalar longitudinal (SL) correlations in PPTA DR2. Therefore, we place $95%$ upper limit on the amplitude of each polarization mode as $mathcal{A}_{mathrm{TT}} lesssim 3.2times 10^{-15}$, $mathcal{A}_{mathrm{ST}} lesssim 1.8times 10^{-15}$, $mathcal{A}_{mathrm{VL}}lesssim 3.5times 10^{-16}$ and $mathcal{A}_{mathrm{SL}}lesssim 4.2times 10^{-17}$; or equivalently, the $95%$ upper limit on the energy density parameter per logarithm frequency as $Omega_{mathrm{GW}}^{mathrm{TT}} lesssim 1.4times 10^{-8}$, $Omega_{mathrm{GW}}^{mathrm{ST}} lesssim 4.5times 10^{-9}$, $Omega_{mathrm{GW}}^{mathrm{VL}} lesssim 1.7times 10^{-10}$ and $Omega_{mathrm{GW}}^{mathrm{SL}} lesssim 2.4times 10^{-12}$ at frequency of 1/year.
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 modelin
g the GWB as a power-law spectrum, we find strong Bayesian evidence for a spatially correlated process with scalar transverse (ST) correlations whose Bayes factor versus the spatially uncorrelated common-spectrum process is $99pm 7$, 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 $Omega_{mathrm{GW}}^{mathrm{ST}} = 1.54^{+1.20}_{-0.71} times 10^{-9}$, at frequency of 1/year.
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 ga
uge, and we find that the energy density spectra of SIGWs, $ogw(k)$, are identical in these three different gauges.
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 s
oon 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 $[2 times 10^{-3}, 7times 10^{-1}] Msun$.
We analytically calculate the scalar induced gravitational waves (SIGWs) and find a log-dependent slope of SIGW in the infrared regions $(f<f_c)$, namely $n_{mathrm{GW}}(f)=3-2/ln(f_c/f)$, and $n_{mathrm{GW}}(f)=2-2/ln(f_c/f)$ near the peak if the po
wer spectrum of scalar curvature perturbation is quite narrow, where $f_c$ is roughly the frequency at the peak of SIGW. Such a log-dependent slope can be taken as a new template for distinguishing SIGW from other sources.
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 primord
ial gravitational-wave spectrum, and forecast how the future observations can improve the current constraint.
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.
