Thick brane in mimetic $f(T)$ gravity

TL;DR

This paper explores thick brane models within mimetic $f(T)$ gravity, analyzing stability, localization, and effects of different $f(T)$ forms, demonstrating four-dimensional gravity recovery and torsion effects on zero modes.

Contribution

It introduces solutions for thick branes in mimetic $f(T)$ gravity using Lagrange multipliers and studies their stability and gravity localization.

Findings

Four-dimensional gravity can be recovered for all solutions.

Polynomial $f(T)$ causes zero mode splitting, exponential form does not.

Stability is confirmed through tensor perturbations.

Abstract

We apply the mimetic $f(T)$ theory into the thick brane model. We take the Lagrange multiplier formulation of the action and get the corresponding field equations of motion. We find solutions for different kinds of $f(T)$. Besides, we investigate the stability of the mimetic $f(T)$ brane by considering the tensor perturbations of the vielbein. Localization problem is also studied and it is shown that the four-dimensional gravity can be recovered for all the solutions. The effects of the torsion show that for the polynomial form of $f(T)$, the zero mode has a split compared with that of $f(T)=T$, but the situations for the exponential form of $f(T)$ are similar to that of $f(T)=T$.