First-order formalism for thick branes in $f(T,\mathcal{T})$ gravity

TL;DR

This paper explores thick brane models within $f(T, ext{ extcal{T}})$ gravity, deriving analytical solutions with scalar fields, analyzing brane splitting phenomena, and studying gravitational perturbations to understand mode localization and stability.

Contribution

It introduces a first-order formalism for thick branes in $f(T, ext{ extcal{T}})$ gravity and provides new analytical solutions demonstrating brane splitting and mode localization.

Findings

Double-kink solutions induce brane splitting.

Torsion parameter influences the brane structure and mode localization.

Massless modes become more localized with parameter adjustments.

Abstract

In this paper, we study the thick brane scenario constructed in the recently proposed $f(T,\mathcal{T})$ theories of gravity, where $T$ is called the torsion scalar, and $\mathcal{T}$ is the trace of the energy-momentum tensor. We use the first-order formalism to find analytical solutions for models that include a scalar field as a source. In particular, we describe two interesting cases in which, in the first, we obtain a double-kink solution, which generates a splitting in the brane. In the second case, proper management of a kink solution obtained generates a splitting in the brane intensified by the torsion parameter, evinced by the energy density components satisfying the weak and strong energy conditions. In addition, we investigate the behavior of the gravitational perturbations in this scenario. The parameters that control the torsion and the trace of the energy-momentum tensor tend to shift the massive modes to the core of the brane, keeping a gapless non-localizable and stable tower of massive modes and producing more localized massless modes.