Cosmologies of Multiple Spherical Brane-universe Model

TL;DR

This paper develops a model of multiple spherical branes in higher-dimensional spacetime, deriving their cosmological evolution and analyzing conditions for different universe behaviors including oscillation, expansion, or collapse.

Contribution

It introduces a new framework for analyzing brane-universe cosmology with spherical topology, including analytical and numerical solutions for various dynamical scenarios.

Findings

Derived effective Friedmann-Robertson-Walker metric for spherical branes.

Identified pressure conditions for oscillating, expanding, or collapsing universes.

Calculated minimum mass to prevent black hole formation in brane scenarios.

Abstract

The Friedmann-Robertson-Walker metric with spherical topology is calculated as an effective metric at the brane in a multiple branes in $D-$dimensional spacetime scenario. In this model the radius of the brane is the cosmological scale factor, and its evolution is calculated from the viewpoint of the observers on their respective branes. The cosmology of the brane-universe is analyzed in cases where the anisotropic pressure has a cosmological constant like state equation. The pressure values needed to distinguish the oscillating, expanding or collapsing solutions are found, and the minimum value of a brane-universe mass to prevent a collapse into a black hole is also calculated. Finally the equation of motion is solved numerically in order to illustrate the different cosmological scenarios and to validate the analytical results.