Smoking guns of a bounce in modified theories of gravity through the spectrum of the gravitational waves

TL;DR

This paper investigates how a bounce in a modified gravity inflationary model influences the gravitational wave spectrum, revealing distinctive low-frequency oscillatory signals that could serve as signatures of such theories.

Contribution

It introduces a bounce-inflation model within $f(R)$ gravity and analyzes its gravitational wave spectrum, highlighting unique low-frequency oscillations as potential observational signatures.

Findings

Distinctive oscillatory signals at low frequencies in the gravitational wave spectrum.

Modified gravity effects are prominent only during the early universe stages.

The spectrum shows unique features that could differentiate $f(R)$ models from standard inflation.

Abstract

We present an inflationary model preceded by a bounce in a metric theory a l\'{a} $f(R)$ where $R$ is the scalar curvature of the space-time. The model is asymptotically de Sitter such that the gravitational action tends asymptotically to a Hilbert-Einstein action, therefore modified gravity affects only the early stages of the universe. We then analyse the spectrum of the gravitational waves through the method of the Bogoliubov coefficients by two means: taking into account the gravitational perturbations due to the modified gravitational action in the $f(R)$ setup and by simply considering those perturbations inherent to the standard Hilbert-Einstein action. We show that there are distinctive (oscillatory) signals on the spectrum for very low frequencies; i.e. corresponding to modes that are currently entering the horizon.