Palatini approach to modified f(R) gravity and its bi-metric structure

TL;DR

This paper explores the conformal symmetries in Palatini f(R) gravity, revealing how the conformal structure relates to the bi-metric nature of the theory and its implications for cosmic acceleration.

Contribution

It analyzes the conformal Killing vectors in flat FLRW spacetime within Palatini f(R) gravity, highlighting their connection to the bi-metric structure and conformal functions.

Findings

Conformal Killing vectors are linked to the new metric h in Palatini f(R) gravity.

Each conformal Killing vector corresponds to a different conformal function.

The study elucidates the conformal symmetry structure in flat FLRW spacetime.

Abstract

f(R) gravity theories in the Palatini formalism has been recently used as an alternative way to explain the observed late-time cosmic acceleration with no need of invoking either dark energy or extra spatial dimension. However, its applications have shown that some subtleties of these theories need a more profound examination. Here we are interested in the conformal aspects of the Palatini approach in extended theories of gravity. As is well known, extremization of the gravitational action a la Palatini, naturally "selects" a new metric h related to the metric g of the subjacent manifold by a conformal transformation. The related conformal function is given by the derivative of f(R). In this work we examine the conformal symmetries of the flat (k=0) FLRW spacetime and find that its Conformal Killing Vectors are directly linked to the new metric h and also that each vector yields a different conformal function.