Semi-transparent brane-worlds

TL;DR

This paper investigates how semi-transparent branes in a brane-world cosmology evolve under Hawking radiation, revealing a critical transmission rate where radiation effects balance gravitational effects, influencing recollapse times.

Contribution

It introduces a detailed analysis of the impact of partial radiation transmission on brane evolution, identifying conditions for critical-like behavior and maximal transmission rates.

Findings

Critical-like behavior occurs at low transmission rates.

Lighter branes recollapse slower, heavier branes faster.

High transmission rates accelerate recollapse.

Abstract

We study the evolution of a closed Friedmann brane perturbed by the Hawking radiation escaping a bulk black hole. The semi-transparent brane absorbes some of the infalling radiation, the rest being transmitted across the brane to the other bulk region. We characterize the cosmological evolution in terms of the transmission rate $\epsilon$. For small values of $\epsilon $ a critical-like behaviour could be observed, when the acceleration due to radiation pressure and the deceleration induced by the increasing self-gravity of the brane roughly compensate each other, and cosmological evolution is approximately the same as without radiation. Lighter (heavier) branes than those with the critical energy density will recollapse slower (faster). This feature is obstructed at high values of $\epsilon $, where the overall effect of the radiation is to speed-up the recollapse. We determine the maximal value of the transmission rate for which the critical-like behaviour is observed. We also study the effect of transmission on the evolution of different source terms of the Friedmann equation. We conclude that among all semi-transparent branes the slowest recollapse occurs for light branes with total absorption.