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arXiv · 2305.04011

Legendre scalarization in gravity and cosmology

Spiros Cotsakis·Jose P. Mimoso·John Miritzis
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Abstract

We propose a new formulation of $f(R)$ gravity, dubbed scalarized $f(R)$ gravity, in which the Legendre transform is included as a dynamical term. This leads to a theory with second-order field equations that describes general relativity with a self-interacting scalar field, without requiring the introduction of conformal frames. We demonstrate that the quadratic version of scalarized $f(R)$ gravity reduces to general relativity with a massive scalar field, and we explore its implications for Friedmann cosmology. Our findings suggest that scalarized $f(R)$ gravity may lead to simplified descriptions of cosmological applications, while the proposed formulation could offer a new perspective on the relationship between $f(R)$ gravity and scalar-tensor theories.

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Spiros Cotsakis, Jose P. Mimoso, John Miritzis. 2023-05-06. Legendre scalarization in gravity and cosmology. https://doi.org/10.1140/epjc%2Fs10052-023-11628-2

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