For a variety of on-going and planned gravitational-wave (GW) experiments, we study expected constraints on the fraction (fPBH) 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 the binary PBHs. The second one is induced through non-linear mode couplings of large primordial curvature perturbations inevitably associated with the generation of PBHs in the early Universe. In this paper, we focus on the PBHs with their masses of 10 −8 M ≤ MPBH < 1M , since they are not expected to be of a stellar origin. In almost all ranges of the masses, we show that the experiments are sensitive to constrain the fraction for 10 −5 fPBH 1 by considering the GWs from coalescing events and 10 −13 fPBH 1 by considering the GWs from curvature perturbations. Exceptionally, only in a narrow range of masses for MPBH 10 −7 M , the fraction cannot be constrained for fPBH 10 −13 by those two GW backgrounds.

We probe the possible anisotropy of the Universe by using the JLA compilation of type-Ia supernovae. We apply the Markov Chain Monte Carlo (MCMC) method to constrain the amplitude and direction of anisotropy in three cosmological models. For the dipole-modulated ΛCDM model, the anisotropic amplitude is consistent with zero at 68% C.L., and has an upper bound A D < 1.98 × 10 −3 at 95% C.L. Regardless of much larger uncertainty, we find the dipole direction of JLA is amazingly opposite to that of Union2. Similar results are found for the dipole-modulated wCDM and CPL models. Thus, the Universe is still well consistent with the isotropy according to the JLA compilation.

We suggest the universe is Finslerian in the stage of inflation. The Finslerian background spacetime breaks rotational symmetry and induces parity violation. The primordial power spectrum is given for the quantum fluctuation of the inflation field. It depends not only on the magnitude of the wavenumber but also on the preferred direction. We derive the gravitational field equations in the perturbed Finslerian background spacetime, and we obtain a conserved quantity outside the Hubble horizon. The angular correlation coefficients are presented in our anisotropic inflation model. The parity violation feature of Finslerian background spacetime requires that the anisotropic effect only appears in the angular correlation coefficients if l = l + 1. The numerical results of the angular correlation coefficients are given describing the anisotropic effect.

The observations on galaxy rotation curves show significant discrepancies from the Newtonian theory. This issue could be explained by the effect of the anisotropy of the spacetime. Conversely, the spacetime anisotropy could also be constrained by the galaxy rotation curves. Finsler geometry is a kind of intrinsically anisotropic geometry. In this paper, we study the effect of the spacetime anisotropy at galactic scales in the Finsler spacetime. It is found that the Finslerian model has close relations with the Milgrom's MOND. By performing the best-fit procedure to the galaxy rotation curves, we find that the anisotropic effects of the spacetime become significant when the Newtonian acceleration GM/r 2 is smaller than the critical acceleration a 0 . Interestingly, the critical acceleration a 0 , although varies between different galaxies, is in the order of magnitude cH 0 /2π ∼ 10 −10 m s −2 .