Effects of a Pre-inflationary de Sitter Bounce on the Primordial Gravitational Waves in $f(R)$ Gravity Theories

TL;DR

This paper investigates how a pre-inflationary de Sitter bounce influences the primordial gravitational wave spectrum within $f(R)$ gravity frameworks, highlighting potential detectability by future gravitational wave experiments.

Contribution

It models a complex cosmological evolution with multiple $f(R)$ gravity patches, demonstrating the impact of a pre-inflationary bounce on gravitational wave signals and their potential observability.

Findings

Primordial gravitational wave spectrum is affected by the de Sitter bounce.

The bounce signal could be detected by future gravitational wave experiments.

Specific $f(R)$ models can realize the entire evolution history.

Abstract

In this work we examine the effects of a pre-inflationary de Sitter bounce on the energy spectrum of the primordial gravitational waves. Specifically we assume that the Universe is described by several evolution patches, starting with a de Sitter pre-inflationary bounce which is followed by an quasi-de Sitter slow-roll inflationary era, followed by a constant equation of state parameter abnormal reheating era, which is followed by the radiation and matter domination eras and the late-time acceleration eras. The bounce and the inflationary era can be realized by vacuum $f(R)$ gravity and the abnormal reheating and the late-time acceleration eras by the synergy of $f(R)$ gravity and the prefect matter fluids present. Using well-known reconstruction techniques we find which $f(R)$ gravity can realize each evolution patch, except from the matter and radiation domination eras which are realized by the corresponding matter fluids. Accordingly, we calculate the damping factor of the primordial de Sitter bounce, and as we show, the signal can be detected by only one gravitational wave future experiment, in contrast to the case in which the bounce is absent. We discuss in detail the consequences of our results and the future perspectives.