Thick branes in Horndeski gravity

TL;DR

This paper explores thick brane solutions within Horndeski gravity, deriving analytical solutions using a first-order formalism for two scalar fields, and analyzes gravity fluctuations to assess four-dimensional gravity corrections.

Contribution

It presents the first analytical solutions for thick branes in Horndeski gravity using a novel two-scalar-field approach and evaluates gravity fluctuations for the first time in this context.

Findings

Found analytical thick brane solutions in Horndeski gravity.

Identified almost massless modes affecting Newtonian potential.

Evaluated limits of four-dimensional gravity with these modes.

Abstract

We investigate thick brane solutions in the Horndeski gravity. In this setup, we found analytical solutions, applying the first-order formalism to two scalar fields where the first field comes from the non-minimal scalar-tensor coupling and the second is due to the matter contribution sector. With these analytical solutions, we evaluate the symmetric thick brane solutions in Horndeski gravity with four-dimensional geometry. In such a setup, we evaluate the gravity fluctuations to find ``almost massless modes'', for any values of the Horndeski parameters. These modes were used to compute the corrections to the Newtonian potential and evaluate the limit four-dimensional gravity.