Robustness of braneworld scenarios against tensorial perturbations

TL;DR

This paper demonstrates that thick brane models in a broad class of metric-affine gravity theories are stable under tensor perturbations, with zero modes matching those of Einstein's gravity, indicating robustness of these scenarios.

Contribution

It shows that tensorial perturbations in general metric-affine gravity theories have a non-negative spectrum and identical zero modes to Einstein's theory, regardless of the specific Lagrangian form.

Findings

Tensor perturbations are stable with non-negative spectrum.

Zero modes match Einstein's gravity predictions.

Stability holds for a wide class of gravity Lagrangians.

Abstract

Inspired by the peculiarities of the effective geometry of crystalline structures, we reconsider thick brane scenarios from a metric-affine perspective. We show that for a rather general family of theories of gravity, whose Lagrangian is an arbitrary function of the metric and the Ricci tensor, the background and scalar field equations can be written in first-order form, and tensorial perturbations have a non negative definite spectrum, which makes them stable under linear perturbations regardless of the form of the gravity Lagrangian. We find, in particular, that the tensorial zero modes are exactly the same as predicted by Einstein's theory regardless of the scalar field and gravitational Lagrangians.