General perturbations in D+1 standard and brane cosmology revisited

TL;DR

This paper extends the theory of cosmological perturbations to higher-dimensional D+1 spacetimes, including brane cosmology, providing equations in different gauges and demonstrating applications to brane-world scenarios and cosmological tensions.

Contribution

It generalizes perturbation theory to D+1 dimensions and brane cosmology, offering new equations and methods applicable to complex cosmological models.

Findings

Derived perturbation equations in Newtonian and Synchronous gauges for D+1 dimensions.

Extended the theory to include brane cosmology with embedded branes.

Applied the framework to analyze energy flux and brane-world implications.

Abstract

In the present work, we generalize the theory of perturbations in a D + 1 dimensional space-time with cosmological constant, studying scalar, vector and tensor perturbations, as well as its structure in Newtonian and Synchronous gauge. We also show the theory of perturbations in the context of brane cosmology, where branes are embedded in a set of D-spatial dimensions, a temporal dimension, and an additional spatial dimension. In both, standard and brane cosmology an unperturbed spacetime is provided with a Friedmann-Lemaitre-Robertson-Walker metric and arbitrary sectional curvature, the matter content has the shape of a perfect fluid. In addition, we consider the arbitrary sectional curvature, obtaining the respective equations in the Newtonian and Synchronous gauge. We highlight that the results presented in this article can be used to treat brane cosmology with two concentric branes or tackle the \sigma_{8} tension with a braneworld approach. Finally, as an example of the utility of all the technology presented in this paper, we show an application to the energy ux and the repercussions in the framework of the brane-worlds.