Detecting the dark sector through scalar-induced gravitational waves

We investigate the evolution of cosmological scalar perturbations in the case that the background radiation is weakly coupled to a light scalar field \(\phi\). The light scalar \(\phi\) is a homogeneous background field with a large initial value. In the radiation-dominated Universe, the coupling term introduces an effective mass to \(\phi\) and the background ultra-relativistic particles. The oscillations of \(\phi\) result in the periodic change of the equation of state parameter and the sound speed, which provides a novel mechanism to amplify subhorizon scalar perturbations through parametric resonance. The amplification of scalar perturbations leads to a stochastic gravitational-waves background~(SGWB) expected to be observed by multiband gravitational wave observers. The observation of the SGWB helps to determine the initial value of \(\phi\) and the coupling strength of the interaction. This mechanism is generally applicable to the interactions that introduce an effective mass, and we take the interaction between \(\phi\) and electrons as a concrete example to illustrate the result. We find that under the condition that the coupling coefficient \(\lambda=10^{-16}\) and the initial value \(\phi_i=10^{18}\) GeV, the resulting SGWB spectrum is expected to be observed by the future observers including LISA, \(Taiji\), DECIGO and BBO.