Construction of Multiple Spherical Branes Cosmological Scenario

TL;DR

This paper develops a comprehensive model of multiple spherical branes in higher-dimensional gravity, analyzing their dynamics, effective mass contributions, and potential cosmological implications, especially in a five-dimensional universe context.

Contribution

It provides a new exact solution for multiple spherical branes with variable cosmological constants and explores their evolution and phenomenology in a higher-dimensional setting.

Findings

Effective mass of branes influenced by cosmological constant differences.

Brane dynamics depend on their equations of state and matter dominance eras.

Derived the Randall-Sundrum metric in a flat brane limit.

Abstract

The general solution of Einstein's gravity equation in $D$ dimensions for an anisotropic and spherically symmetric matter distribution is calculated in a bulk with position dependent cosmological constant. Results for $n$ concentric $(D-2)-$branes with arbitrary mass, radius and pressure with different cosmological constant between branes are found. It is shown how the difference between the cosmological constant contributes to the effective mass of each brane, and it is also shown that the equation of state for each brane influences the dynamics of branes, which can be divided into eras according to the dominant matter. This scenario can be used to model the universe in the D=5 case, which may presents a richer phenomenology than the current models. The evolution law of the branes is studied, and the anisotropic pressure that remove divergences is found. The Randall-Sundrum metric in an outside region in the flat branes limit is also derived.