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arXiv · 2412.09366

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

Adrián Casado-Turrión·Álvaro de la Cruz-Dombriz·Antonio Dobado
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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.

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Adrián Casado-Turrión, Álvaro de la Cruz-Dombriz, Antonio Dobado. 2024-12-12. Propagating degrees of freedom on maximally-symmetric backgrounds in $f(R)$ theories of gravity. https://arxiv.org/abs/2412.09366

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