Effects of quantum fluctuations of the metric on a braneworld

TL;DR

This paper explores how quantum metric fluctuations affect the dynamics and stability of thick branes in a modified gravity framework, revealing their impact on vacuum states, energy profiles, and matter configurations.

Contribution

It introduces a model where quantum metric fluctuations induce an $f(R,T)$ gravity, analyzing their effects on brane stability and matter field configurations using differential configurational entropy.

Findings

Quantum fluctuations modify brane vacuum states.

Metric fluctuations influence matter field profiles.

Stable brane structures are identified through configurational entropy.

Abstract

Adopting the premise that the expected value of the quantum fluctuating metric is linear, i.e., $\langle g^{\mu\nu}\rangle=\alpha g^{\mu\nu}$, we analyze the modified gravity theory induced by the Einstein-Hilbert action coupled to a matter field. This approach engenders the $f(R,T)$ gravity used to investigate the braneworld. In this scenario, considering a thick brane, the influence of metric fluctuations on brane dynamics is investigated. Consequently, one shows how the metric fluctuations influence the vacuum states. This influence has repercussions for modifying the brane energy and the asymptotic profile of the matter field. After noticing these modifications, we analyzed the most likely and stable structures from the matter field. One performs this analysis considering the theoretical measure of differential configurational entropy.