Advanced LIGO’s discovery of gravitational-wave events is stimulating extensive studies on the origin of binary black holes. Assuming that the gravitational-wave events can be explained by binary primordial black hole mergers, we utilize the upper limits on the stochastic gravitational-wave background given by Advanced LIGO as a new observational window to independently constrain the abundance of primordial black holes in dark matter. We show that Advanced LIGO’s first observation run gives the best constraint on the primordial black hole abundance in the mass range $1{\mathit{M}}_{\odot }\lesssim M_{\mathrm{PBH}}\lesssim 100{\mathit{M}}_{\odot }$, pushing the previous microlensing and dwarf galaxy dynamics constraints tighter by 1 order of magnitude. Moreover, we discuss the possibility to detect the stochastic gravitational-wave background from primordial black holes, in particular from subsolar mass primordial black holes, by Advanced LIGO in the near future.

For a variety of ongoing and planned gravitational-wave (GW) experiments, we study expected constraints on the fraction ($f_{\mathrm{PBH}}$) of primordial black holes (PBHs) in dark matter by evaluating the energy-density spectra of two kinds of stochastic GW backgrounds. The first one is produced from an incoherent superposition of GWs emitted from coalescences of all of the binary PBHs. The second one is induced through nonlinear mode couplings of large primordial curvature perturbations inevitably associated with the generation of PBHs in the early Universe. In this paper, we focus on PBHs with masses ${10}^{-8}{M}_{\odot }\le M_{\mathrm{PBH}}<1M_{\odot }$, since they are not expected to be of stellar origin. In almost all mass ranges, we show that the experiments are sensitive enough to constrain the fraction for ${10}^{-5}\lesssim f_{\mathrm{PBH}}\lesssim 1$ by considering the GWs from coalescing events and ${10}^{-13}\lesssim f_{\mathrm{PBH}}\lesssim 1$ by considering the GWs from curvature perturbations. Exceptionally, the fraction cannot be constrained for $f_{\mathrm{PBH}}\lesssim {10}^{-3}$ by these two GW backgrounds only in the narrow mass range around $M_{\mathrm{PBH}}\simeq {10}^{-7}{M}_{\odot }$.

Multiple pulsar-timing-array collaborations have reported strong evidence for the existence of a gravitational-wave background. We study physical implications of this signal for cosmology, assuming that it is attributed to scalar-induced gravitational waves. By incorporating primordial non-Gaussianity $f_{\mathrm{NL}}$, we specifically examine the nature of primordial curvature perturbations and primordial black holes. We find that the signal allows for a primordial non-Gaussianity $f_{\mathrm{NL}}$ in the range of $-4.1\lesssim f_{\mathrm{NL}}\lesssim 4.1$ (68% confidence intervals) and a mass range for primordial black holes $m_{\mathrm{pbh}}$ spanning from $\sim {10}^{-5}{M}_{\odot }$ to $\sim {10}^{-2}{M}_{\odot }$. Furthermore, we find that the signal favors a negative non-Gaussianity, which can suppress the abundance of primordial black holes. We also demonstrate that the anisotropies of scalar-induced gravitational waves serve as a powerful tool to probe the non-Gaussianity $f_{\mathrm{NL}}$. We conduct a comprehensive analysis of the angular power spectrum within the nano-Hertz band. Looking ahead, we anticipate that future projects, such as the Square Kilometre Array, will have the potential to measure these anisotropies and provide further insights into the primordial universe.

The local measurement of H₀ is in tension with the prediction of Λ cold dark matter model based on the Planck data. This tension may imply that dark energy is strengthened in the late-time Universe. We employ the latest cosmological observations on cosmic microwave background, the baryon acoustic oscillation, large-scale structure, supernovae, H(z) and H₀ to constrain several interacting dark energy models. Our results show no significant indications for the interaction between dark energy and dark matter. The H₀ tension can be moderately alleviated, but not totally released.

Taking into account the mass splittings between three active neutrinos, we investigate the impacts of dark energy on constraining the total neutrino mass $\sum m_{\nu }$ by using recent cosmological observations. We consider two typical dark energy models, namely, the $w\mathrm{CDM}$ model and the holographic dark energy (HDE) model, which both have an additional free parameter compared with the $\mathrm{\Lambda }\mathrm{CDM}$ model. We employ the Planck 2015 data of CMB temperature and polarization anisotropies, combined with low-redshift measurements on BAO distance scales, type Ia supernovae, the Hubble constant, and Planck lensing. Compared to the $\mathrm{\Lambda }\mathrm{CDM}$ model, our study shows that the upper limit on $\sum m_{\nu }$ becomes much looser in the $w\mathrm{CDM}$ model but much tighter in the HDE model. In the HDE model, we obtain the 95% confidence level upper limit $\sum m_{\nu }<0.105\mathrm{eV}$ for three degenerate neutrinos. This might be the most stringent constraint on $\sum m_{\nu }$ by far, and it is on the verge of diagnosing the neutrino mass hierarchies in the HDE model. However, the difference of ${\chi }^2$ is still not significant enough to distinguish the neutrino mass hierarchies, even though the minimal ${\chi }^2$ of the normal hierarchy is slightly smaller than that of the inverted hierarchy.