Sound speed resonance of the stochastic gravitational waves background

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 the tensor perturbation, while the cosmological background evolution is the same as the one in GR with $\Lambda \text{CDM}$ 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.