We report on a novel phenomenon of the resonance effect of primordial density perturbations arisen from a sound speed parameter with an oscillatory behavior, which can generically lead to the formation of primordial black holes in the early Universe. For a general inflaton field, it can seed primordial density fluctuations, and their propagation is governed by a parameter of sound speed square. Once, if this parameter achieves an oscillatory feature for a while during inflation, a significant nonperturbative resonance effect on the inflaton field fluctuations takes place around a critical length scale, which results in significant peaks in the primordial power spectrum. By virtue of this robust mechanism, primordial black holes with specific mass function can be produced with a sufficient abundance for dark matter in sizable parameter ranges.

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.

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We propose a novel mechanism to amplify the primordial gravitational waves (GWs) at the scale which can be detected by current or near future gravitational wave detectors. In many theories of modified gravity, the sound speed of gravitational waves receives a time-dependent modification and thus deviates from unity. We investigate a class of scalar-tensor theories of which modification primarily affects tensor perturbations, while the cosmological background evolution and the linear scalar perturbations are the same as the ones in GR with ΛCDM ingredients. We report that, one featured phenomenon of the varying GW speed cosmology is that the energy spectrum of GWs can present the resonantly enhanced peaks due to a short period of oscillatory behaviour for the GW speed at high-energy scales. This oscillatory behaviour may come from the coherent oscillation of the scalar degree during the early epoch of the universe. The frequencies, as well as the amplitudes of these peaks can be constrained/detected by the current and forthcoming GW experiments.