Novel modified gravity braneworld configurations with a Lagrange multiplier

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.

Automated summary

In this work, the authors investigate thick brane solutions in the context of modified gravity theories with a Lagrange multiplier, focusing on using a single scalar field to represent warp functions and uncovering specific symmetric and asymmetric brane configurations. Including a Lagrange multiplier offers an alternative approach to inducing brane structures using a single scalar field, opening up new avenues of research in braneworld scenarios and resulting in interesting outcomes for matter field localization on the brane.