Propagating degrees of freedom on maximally-symmetric backgrounds in $f(R)$ theories of gravity

TL;DR

This paper investigates the dynamical modes in $f(R)$ gravity models on maximally-symmetric backgrounds, revealing that degenerate models lack both graviton and scalaron modes, unlike non-degenerate models.

Contribution

It provides a consistent method to analyze degrees of freedom in $f(R)$ gravity, extending previous results to a broader class of degenerate models and clarifying their spectrum.

Findings

Degenerate $f(R)$ models have no dynamical modes on maximally-symmetric backgrounds.

Non-degenerate models exhibit both graviton and scalaron modes.

Pathologies in degenerate models are universal across the class.

Abstract

In the context of $f(R)$ gravity, as well as other extended theories of gravity, the correct counting of globally well-defined dynamical modes has recently drawn a vivid interest. In this communication we present a consistent approach shedding light on such issues for both so-called degenerate and non-degenerate $f(R)$ models embedded in maximally-symmetric backgrounds. We find that the linearised spectrum of degenerate models on these backgrounds is empty, lacking both the graviton and scalaron modes which appear in generic non-degenerate models. Our work generalises previous results in the literature applicable only to the specific (degenerate) model $f(R)=\alpha R^2$; in fact, we find that the same pathologies discovered therein emerge for all choices of $f(R)$ belonging to the wide class of degenerate models.