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

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.

31 pages, 49 figures. Revised version to match published version in EPJC

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• Constraining extended teleparallel gravity via cosmography: A model-independent approach
• Localization of abelian gauge fields with Stueckelberg-like geometrical coupling on $f(T,B)$-thick brane
• Quasinormal modes and echoes of a double braneworld
• 5D Elko spinor field non-minimally coupled to nonmetricity in $f(Q)$ gravity
• Characteristic modes of thick brane model: resonances and quasinormal modes
• Geometrically contracted structure in teleparallel $f(T)$ gravity
• New class of solutions in the non-minimal O(3)-sigma model
• Differential configurational entropy for multi-field of the ${\varphi }^6$ theory
• Graviscalar quasinormal modes and asymptotic tails of a thick brane
• Linear Perturbations and Stability Analysis in $f(T)$ Braneworld Scenario