Full linear perturbations and localization of gravity on $f(R,T)$ brane

TL;DR

This paper investigates the effects of $f(R,T)$ gravity on thick brane models, analyzing linear perturbations and gravity localization, revealing modifications to scalar modes while preserving the massless tensor mode for effective gravity.

Contribution

It introduces analytic solutions for $f(R,T)$ brane models and examines how scalar perturbations differ from general relativity, ensuring gravity localization without tachyon states.

Findings

Scalar perturbation modes are modified in $f(R,T)$ models.

Only the massless tensor mode is localized, recovering 4D gravity.

No tachyon states are present in the model.

Abstract

We study the thick brane world system constructed in the recently proposed $f(R,T)$ theories of gravity, with $R$ the Ricci scalar and $T$ the trace of the energy-momentum tensor. We try to get the analytic background solutions and discuss the full linear perturbations, especially the scalar perturbations. We compare how the brane world model is modified with that of general relativity coupled to a canonical scalar field. It is found that some more interesting background solutions are allowed, and only the scalar perturbation mode is modified. There is no tachyon state exists in this model and only the massless tensor mode can be localized on the brane, which recovers the effective four-dimensional gravity. These conclusions hold provided that two constraints on the original formalism of the action are satisfied.