Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity

TL;DR

This paper develops a framework to study scalar-induced gravitational waves in Palatini $f(R)$ gravity, showing how their spectrum differs from General Relativity and metric $f(R)$ models, with implications for upcoming gravitational wave observations.

Contribution

It introduces a general method for analyzing scalar-induced gravitational waves in Palatini $f(R)$ gravity and compares the spectral predictions to other gravity theories.

Findings

Spectral density differs from GR and metric $f(R)$ predictions under certain conditions.

Provides analytical expressions for the kernel function and density spectrum.

Highlights the potential of gravitational wave observations to distinguish gravity formalisms.

Abstract

Primordial scalar perturbations that reenter the horizon after inflation may induce a second-order Gravitational Wave spectrum with information about the primordial Universe on scales inaccessible to Cosmic Microwave Background experiments. In this work, we develop a general framework for the study of Scalar-Induced Gravitational Waves in Palatini $f(R)$ gravity, a theory that was proven to successfully realise inflation and quintessence, and consider the case of the Starobinsky-like model as an example. A regime of radiation domination with a subdominant matter component is assumed, allowing for a well-motivated perturbative approach to the gravity modifications. We calculate the kernel function and the density spectrum numerically and find accurate analytical expressions. The spectral density, which may be tested across a wide range of frequencies by upcoming Gravitational Wave experiments, is shown to differ from the General Relativity and metric $f(R)$ gravity predictions under certain conditions. We comment on previous results in the literature regarding the metric formulation and make special emphasis on the potential of these distinctive features of the spectrum to probe the two formalisms of gravity.