# Constraints on generalized Eddington-inspired Born-Infeld branes

Lin, Zi-Chao (Institute of Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China) ; Yang, Ke (School of Physical Science and Technology, Southwest University, Chongqing 400715, China) ; Zhang, Yu-Peng (Institute of Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China) ; Wang, Jian (Institute of Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China) ; Liu, Yu-Xiao (Institute of Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China) (Key Laboratory for Magnetism and Magnetic of the Ministry of Education, Lanzhou University, Lanzhou 730000, China)

13 April 2019

Abstract: The Palatini $f\left(|\stackrel{^}{\Omega }|\right)$ gravity is a generalized theory of the Eddington-inspired Born-Infeld gravity, where ${{\Omega }^{K}}_{N}\equiv {{\delta }^{K}}_{N}+b{g}^{KL}{R}_{LN}\left(\Gamma \right)$ is an auxiliary tensor constructed with the spacetime metric $g$ and independent connection $\Gamma$. In this paper, we study $f\left(|\stackrel{^}{\Omega }|\right)$ theory with $f\left(|\stackrel{^}{\Omega }|\right)=|\stackrel{^}{\Omega }{|}^{\frac{1}{2}+n}$ in the thick brane scenario and give some constraints on the brane model. We finally found an analytic solution of the thick brane generated by a single scalar field. The behavior of the negative energy density denotes the localization of the thick brane at the origin of the extra dimension. In our braneworld, the warp factor is divergent at the boundary of the extra dimension while the brane system is asymptotically anti–de Sitter. It is shown that the tensor perturbation of the brane is stable and the massless graviton is localized on the thick brane. Therefore, the effective Einstein-Hilbert action on the brane can be rebuilt in the low-energy approximation. According to the recent test of the gravitational inverse-square law, we give some constraints on the $f\left(|\stackrel{^}{\Omega }|\right)$ brane.

Published in: Physical Review D 99 (2019)