Abstract
In this paper we study the thick brane scenario constructed in the recently proposed f(T,{mathscr {T}}) theories of gravity, where T is called the torsion scalar and {mathscr {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 case 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.
Highlights
Known as f (R) gravity [28,29], a change in the usual gravity theory could be considered as an extension of General Relativity (GR), where R is the scalar of curvature
Another possibility would be f (R, T ) gravity, where T is the trace of the energy–momentum tensor [30]
The increasing interest in modified teleparallel gravity and in the significant results obtained in f (T, T ) gravity, that seems as an alternative to GR, inspired us to investigate the impact of torsion (T) and of trace of the energy–momentum tensor (T ) on the structure of branes
Summary
A scalar field, in a modification of the RS model, makes the warp function behave smoothly, leading to a thick braneworld scenario [8,9,10,11,12]. The TEGR is constructed using the Weitzenböck connection instead of the Levi-Civita connection of GR, which leads to a vanishing curvature but a nonvanishing torsion, where the fundamental dynamical quantity of the theory is a tetrad field In such a formulation, the contribution of torsion in the gravitational Lagrangian results from contractions of the torsion tensor and it is called the torsion scalar T. In this work we consider two power-law modified gravity in the form f (T, T ) = k0T +kT n, where k and n are parameters controlling the influence of torsion and k0 controls the influence of the trace of the energy–momentum tensor, and f (T, T ) = −T − k1T 2 + k2T , where k1 is parameter that controls the influence of torsion and k2 controls the influence of the trace of the energy–momentum tensor We chose these particular f (T, T ) models because of their simplicity and inspired by the models proposed in gravity f (R, T ), which can be seen in Refs. We chose these particular f (T, T ) models because of their simplicity and inspired by the models proposed in gravity f (R, T ), which can be seen in Refs. [31,32,33,34]
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