Hybrid metric-Palatini brane system

TL;DR

This paper investigates tensor perturbations of thick branes in hybrid metric-Palatini gravity, demonstrating the stability of the models and the localization of gravity, with one model showing inner structure in the graviton zero mode.

Contribution

It provides the first analysis of tensor perturbations in hybrid metric-Palatini brane models, showing stability and gravity localization in two specific configurations.

Findings

Both models reproduce effective 4D gravity on the brane.

The first model's graviton zero mode develops inner structure above a critical parameter.

Both models are stable against tensor perturbations.

Abstract

It is known that the metric and Palatini formalisms of gravity theories have their own interesting features but also suffer from some different drawbacks. Recently, a novel gravity theory called hybrid metric-Palatini gravity was put forward to cure or improve their individual deficiencies. The action of this gravity theory is a hybrid combination of the usual Einstein-Hilbert action and a $f(\mathcal{R})$ term constructed by the Palatini formalism. Interestingly, it seems that the existence of a light and long-range scalar field in this gravity may modify the cosmological and galactic dynamics without conflicting with the laboratory and Solar System tests. In this paper we focus on the tensor perturbation of thick branes in this novel gravity theory. We consider two models as examples, namely, the thick branes constructed by a background scalar field and by pure gravity. The thick branes in both models have no inner structure. However, the graviton zero mode in the first model has inner structure when the parameter in this model is larger than its critical value. We find that the effective four-dimensional gravity can be reproduced on the brane for both models. Moreover, the stability of both brane systems against the tensor perturbation can also be ensured.