Linear Perturbations and Stability Analysis in $f(T)$ Braneworld Scenario

TL;DR

This paper analyzes linear perturbations in $f(T)$ gravity within braneworld scenarios, showing that only standard degrees of freedom propagate and demonstrating stability for a specific thick brane model.

Contribution

It provides a comprehensive decomposition of perturbations in $f(T)$ braneworlds and shows the absence of extra degrees of freedom compared to general relativity.

Findings

Only scalar, vector, and tensor modes propagate.

No additional degrees of freedom appear in linearized theory.

The $f(T)=T+eta T^2$ model is stable against linear perturbations.

Abstract

We conduct a detailed analysis of the full linear perturbations in the braneworld scenario within $f(T)$ gravity. By decomposing the perturbations of the theory into the scalar, transverse vector, antisymmetric pseudotensor, and symmetric transverse-traceless tensor modes, we derive the quadratic action for each mode. The results indicate that there is a total of one scalar, one massless vector, and one tensor propagating degrees of freedom. Consequently, in comparison to general relativity, no additional degrees of freedom appear under the flat braneworld background in the linearized theory. For a thick brane model with $f(T)=T+ \alpha T^2$, we find that it exhibits stability against linear perturbations.