Legendre scalarization in gravity and cosmology

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.

Automated summary

We propose a new formulation of f(R) gravity, referred to as scalarized f(R) gravity, which incorporates the Legendre transform as a dynamic term. This results in a theory with second-order field equations that describe general relativity with a self-interacting scalar field, without the need for introducing conformal frames. We demonstrate that the quadratic version of scalarized f(R) gravity reduces to general relativity with a massive scalar field, and explore its implications for Friedmann cosmology. Our findings suggest that scalarized f(R) gravity may provide simplified descriptions for cosmological applications, while the proposed formulation offers a new perspective on the relationship between f(R) gravity and scalar-tensor theories.