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

## TL;DR

This paper investigates how a gradual transition from an early matter era to the radiation era affects gravitational waves induced by scalar perturbations, revealing that such a transition does not necessarily amplify these waves as previously thought.

## Contribution

It provides a detailed analysis of the gravitational potential evolution during a gradual transition, challenging prior assumptions about gravitational wave enhancement.

## Key findings

- Early matter era does not always increase induced gravitational waves.
- The gravitational potential decays around the transition, reducing wave amplitude.
- Gradual transition effects differ from instantaneous transition models.

## 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.