Quintessential Einstein-Legendre modified f(R) gravity theory

ABSTRACT: We investigate a new formulation of f(R) gravity, dubbed Einstein-Legendre f(R) gravity, in which a 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 find 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 this scalarized f(R) gravity may lead to simplified description of cosmological applications. The proposed formulation could offer a new perspective on the relationship between f(R) gravity and scalar–tensor theories.