Novel modified gravity braneworld configurations with a Lagrange multiplier

TL;DR

This paper explores thick brane solutions in a five-dimensional warped spacetime within modified gravity theories incorporating a Lagrange multiplier, revealing new brane configurations and stability properties.

Contribution

It introduces a first order framework using a single scalar field to generate symmetric and asymmetric brane structures in modified gravity with a Lagrange multiplier.

Findings

Constructed symmetric and asymmetric brane configurations.

Demonstrated the stability of the gravitational sector.

Showed how a Lagrange multiplier can induce brane structures with a single scalar field.

Abstract

In this work we deal with thick brane solutions in the warped five-dimensional braneworld scenario with a single extra spatial dimension of infinite extent, for a class of modified theories of gravity with a Lagrange multiplier. We first present the action, describe the gravity and field equations, outline a strategy to find explicit solutions and explore the stability of the gravitational sector. The investigation deals mainly with the construction of a first order framework capable of using a single scalar field to simulate warp functions that appear in two-field models. In particular, we find specific symmetric and asymmetric brane configurations that engender asymptotic profiles with symmetric and asymmetric five-dimensional anti-de Sitter geometries. Thus, including a Lagrange multiplier unveils an alternative approach to induce brane structure using a single scalar field, tracing out new avenues of research in braneworld scenarios, naturally leading to interesting results for the localization of matter fields in the brane.