Recently, inspired by Eddington's theory, an alternative gravity called Eddington-inspired Born-Infeld gravity was proposed by Ba\~nados and Ferreira. It is equivalent to Einstein's general relativity in vacuum, but deviates from it when matter is included. Interestingly, it seems that the cosmological singularities are prevented in this theory. Based on the new theory, we investigate a thick brane model with a scalar field presenting in the five-dimensional background. A domain wall solution is obtained, and further, we find that at low energy the four-dimensional Einstein gravity is recovered on the brane. Moreover, the stability of gravitational perturbations is ensured in this model.

In this paper we apply the five-dimensional f(T) gravity with f(T)=T+kTn to brane scenario to explore the solutions under a given warp factor, and we find that the analytic domain wall solution will be a double-kink solution when the geometric effect of spacetime torsion is strongly enhanced. We also investigate the localization of fermion fields on the split branes corresponding to the double-kink solution.

This work tries to find out thick brane solutions in braneworld scenarios described by a real scalar field in the presence of a scalar-kinetic term F(X, )=X^m with a single extra dimension, where stands for the standard kinetic term and m=0, 1, 2... . We mainly consider bent branes, namely de Sitter and anti-de Sitter four-dimensional slices. The solutions of a flat brane are obtained when taking the four-dimensional cosmological constant Λ₄→0. When the parameter m=0, these solutions turn to those of the standard scenario. The localization and spectrum of graviton on these branes are also analyzed.