Abstract
In this paper, we explore the five-dimensional f(T,B) teleparallel modified gravity with f_1(T,B)=T+k_1B^{n_1} and f_2(T,B)=B+k_2T^{n_2} in the brane scenario. Asymptotically, the bulk geometry converges to an AdS_5 spacetime whose cosmological constant is produced by parameters that control torsion and boundary term. The analysis of the energy density condition reveals a splitting brane process satisfying the weak and strong energy conditions for some values of the parameters n_{1,2} and k_{1,2}. In addition, we investigate the behavior of the gravitational perturbations in this scenario. In the bulk, the torsion keeps a gapless non-localizable, and stable tower of massive modes. Inside the brane core, the torsion produces new barriers and potential wells, leading to small amplitude massive modes and a massless mode localized for some values of the parameters n_{1,2} and k_{1,2}.
Highlights
Randall-Sundrum (RS) brane models [1,2] have attracted much attention since they were proposed because of their great success in solving the hierarchy problem [2] and in enabling new approaches to address outstanding issues such as the cosmological problem [3], the nature of dark matter [4], and dark energy
In this paper we explore the five-dimensional fðT; BÞ teleparallel modified gravity with f1ðT; BÞ 1⁄4 T þ k1Bn1 and f2ðT; BÞ 1⁄4 B þ k2Tn2 in the brane scenario
A new approach is the so-called thick brane model, where the brane is constructed by the scalar field [5,6,7,8,9]
Summary
The advantage of this theory is that the equations of motion are of second order, in contrast to the fourth-order equations of fðRÞ gravity Since it is a new gravitational modification class, various thick brane models have been investigated in Refs. Significant results were obtained in cosmological perturbations and thermodynamics, dark energy, and gravitational waves [49,50,51,52,53,54,55] This model provides equivalence between torsion and curvature, where one simultaneously recovers the models of both fðTÞ gravity and fðRÞ 1⁄4 fð−T þ BÞ gravity.
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