Constraints on generalized Eddington-inspired Born-Infeld branes

TL;DR

This paper explores a generalized gravity theory in thick brane models, deriving an analytic solution, analyzing stability, and providing constraints based on gravitational tests, thus advancing understanding of brane-world scenarios in modified gravity.

Contribution

It introduces a specific form of $f(| ext{ extbar}\hat{oldsymbol{ extOmega}} ext{ extbar}|)$ gravity in thick branes, finds an analytic solution, and analyzes stability and observational constraints.

Findings

Analytic thick brane solution with scalar field.

Stable tensor perturbations and localized graviton.

Constraints on the model from gravitational inverse-square law tests.

Abstract

The Palatini $f(|\hat{\Omega}|)$ gravity is a generalized theory of the Eddington-inspired Born-Infeld gravity, where $\Omega_{~N}^{K}\equiv\delta_{~N}^{K}+bg^{KL}R_{LN}(\Gamma)$ is an auxiliary tensor constructed with the spacetime metric $g$ and independent connection $\Gamma$. In this paper, we study $f(|\hat{\Omega}|)$ theory with $f(|\hat{\Omega}|)=|\hat{\Omega}|^{\frac{1}{2}+n}$ 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 $f(|\hat{\Omega}|)$ brane.