Correspondence between Jordan-Einstein frames and Palatini-metric formalisms

TL;DR

This paper explores the relationship between Jordan and Einstein frames in modified gravity, showing their equivalence in degrees of freedom despite different representations, through conformal transformations linking metric and Palatini formalisms.

Contribution

It clarifies the connection between Jordan and Einstein frames in modified gravity, demonstrating the equivalence of their dynamical content across metric and Palatini formalisms.

Findings

Conformal transformations connect Jordan and Einstein frames.

Differences between Palatini and metric formalisms depend on representation.

Number of degrees of freedom remains unchanged.

Abstract

We discuss the conformal symmetry between Jordan and Einstein frames considering their relations with the metric and Palatini formalisms for modified gravity. Appropriate conformal transformations are taken into account leading to the evident connection between the gravitational actions in the two mentioned frames and the Hilbert-Einstein action with a cosmological constant. We show that the apparent differences between Palatini and metric formalisms strictly depend on the representation while the number of degrees of freedom is preserved. This means that the dynamical content of both formalism is identical.