Tensor perturbations in a general class of Palatini theories

TL;DR

This paper investigates tensor perturbations within a broad class of Palatini gravitational theories, revealing that under certain conditions, these perturbations behave similarly to those in Einstein gravity, especially when anisotropic stresses are absent.

Contribution

It derives the evolution equations for tensor perturbations in Palatini theories and establishes their relation to Einstein-like equations in cosmological backgrounds.

Findings

Tensor perturbations follow Einstein-like equations without anisotropic stresses.

Auxiliary metric perturbations coincide with space-time metric perturbations in specific conditions.

The study provides a framework for analyzing gravitational waves in Palatini theories.

Abstract

We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the space-time metric tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.