Legendre scalarization in gravity and cosmology

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.

arXiv commentv2: 14 pages, 3 figures, matches published version

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• Pure geometric $f(R)$ branes
• Friedmann-Lemaître universes and their metamorphoses
• On the "Legendre scalarization" of nonlinear gravity theories