Gravitational Waves Induced by Scalar Perturbations during a Gradual Transition from an Early Matter Era to the Radiation Era

Abstract

We revisit the effects of an early matter-dominated era on gravitational waves induced by scalar perturbations. We carefully take into account the evolution of the gravitational potential, the source of these induced gravitational waves, during a gradual transition from an early matter-dominated era to the radiation-dominated era, where the transition timescale is comparable to the Hubble time at that time. Realizations of such a gradual transition include the standard perturbative reheating with a constant decay rate. Contrary to previous works, we find that the presence of an early matter-dominated era does not necessarily enhance the induced gravitational waves due to the decay of the gravitational potential around the transition from an early matter-dominated era to the radiation-dominated era.

Comments: 14 pages, 5 figures, v3: error in numerical calculation for Figures 4 and 5 corrected, revised Figure 4 showing small-scale induced GWs suppressed more, typo in Eq.(4.3) corrected, conclusion unchanged