Towards a Complete Treatment of Scalar-induced Gravitational Waves with Early Matter Domination

Large curvature perturbations can source an observable amount of stochastic gravitational wave background (SGWB). We consider several scenarios where small-scale curvature perturbations are naturally enhanced due to the presence of additional spectator fields during inflation. The same spectator fields can lead to a period of early matter domination (EMD) after inflation. We compute the inflationary spectrum of curvature perturbation and determine its evolution at later times, taking into account both the onset and the end of the EMD epoch, and also the impact of relative velocity perturbation between matter and radiation. The feature that the same field is responsible for both enhanced perturbations and the EMD era, leads to a predictive framework within which the full frequency dependence of SGWB can be computed. The SGWB can be observed in several detectors, including those focused on the nano-Hz regime. Our numerical framework can also be used to study other non-standard cosmological histories.