Conformal aspects of Palatini approach in Extended Theories of Gravity

TL;DR

This paper explores the physical significance of conformal transformations within the Palatini approach to extended gravity theories, highlighting their role in distinguishing spacetime and geodesic structures and affecting cosmological interpretations.

Contribution

It demonstrates that conformal transformations have a physical meaning in the Palatini framework, especially through the bi-metric structure, impacting the understanding of gravitational and cosmological phenomena.

Findings

Conformal transformations can be physically meaningful in Palatini gravity.

The bi-metric structure distinguishes spacetime and geodesic structures.

Cosmological solutions vary significantly between Einstein and Jordan frames.

Abstract

The debate on the physical relevance of conformal transformations can be faced by taking the Palatini approach into account to gravitational theories. We show that conformal transformations are not only a mathematical tool to disentangle gravitational and matter degrees of freedom (passing from the Jordan frame to the Einstein frame) but they acquire a physical meaning considering the bi-metric structure of Palatini approach which allows to distinguish between spacetime structure and geodesic structure. Examples of higher-order and non-minimally coupled theories are worked out and relevant cosmological solutions in Einstein frame and Jordan frames are discussed showing that also the interpretation of cosmological observations can drastically change depending on the adopted frame.