As potential candidates of dark matter, primordial black holes (PBHs) are within the core scopes of various astronomical observations. In light of the explosive development of gravitational wave (GW) and radio astronomy, we thoroughly analyze a stochastic background of cosmological GWs, induced by overly large primordial density perturbations, with several spikes that was inspired by the sound speed resonance effect and can predict a particular pattern on the mass spectrum of PBHs. With a specific mechanism for PBHs formation, we for the first time perform the study of such induced GWs that originate from both the inflationary era and the radiation-dominated phase. We report that, besides the traditional process of generating GWs during the radiation-dominated phase, the contribution of the induced GWs in the sub-Hubble regime during inflation can become significant at the critical frequency band because of a narrow resonance effect. All contributions sum together to yield a specific profile of the energy spectrum of GWs that can be of observable interest in forthcoming astronomical experiments. Our study shed light on the possible joint probe of PBHs via various observational windows of multimessenger astronomy, including the search for electromagnetic effects with astronomical telescopes and the stochastic background of relic GWs with GW instruments.

We study cosmological perturbation theory within the framework of unimodular gravity. We show that the Lagrangian constraint on the determinant of the metric required by unimodular gravity leads to an extra constraint on the gauge freedom of the metric perturbations. Although the main equation of motion for the gravitational potential remains the same, the shift variable, which is gauge artifact in General Relativity, cannot be set to zero in unimodular gravity. This non-vanishing shift variable affects the propagation of photons throughout the cosmological evolution and therefore modifies the Sachs-Wolfe relation between the relativistic gravitational potential and the microwave temperature anisotropies. However, for adiabatic fluctuations the difference between the result in General Relativity and unimodular gravity is suppressed on large angular scales. Thus, no strong constraints on the theory can be derived.

We study sound speed resonance (SSR) mechanism for primordial black hole (PBH) formation in an early universe scenario with inflaton and curvaton being mixed. In this scenario, the total primordial density perturbations could be contributed by the fluctuations from both the inflaton and curvaton fields, in which the inflaton fluctuations lead to the standard adiabatic perturbations, while the sound speed of the curvaton fluctuations are assumed to be oscillating during inflation. Due to the narrow resonance effect of SSR mechanism, we acquire the enhanced primordial density perturbations on small scales and they remain nearly scale-invariant on large scales, which is essential for PBH formation. Finally, we find that the PBHs with specific mass spectrum can be produced with a sufficient abundance for dark matter in the mixed scenario.

We find static charged black hole solutions in nonlinear massive gravity. In the parameter space of two gravitational potential parameters (α, β) we show that below the Compton wavelength the black hole solutions reduce to that of Reissner-Nordström via the Vainshtein mechanism in the weak field limit. In the simplest case with α = β = 0 the solution exhibits the vDVZ discontinuity but ordinary General Relativity is recovered deep inside the horizon due to the existence of electric charge, though this case is observationally excluded. For α = 0 and β = 0, the post-Newtonian parameter of the charged black hole evolves to that of General Relativity via the Vainshtein mechanism within a macroscopic distance; however, a logarithmic correction to the metric factor of the time coordinate is obtained. When α and β are both nonzero, there exist two branches of solutions depending on the positivity of β. When β < 0, the strong coupling of the scalar graviton weakens gravity at distances smaller than the Vainshtein radius. However, when β > 0 the metric factors exhibit only small corrections compared to the solutions obtained in General Relativity, and under a particular choice of β = α 2 /6 the standard Reissner-Nordström-de Sitter solution is recovered.