Constraints on brane and bulk ideal fluid in Randall-Sundrum cosmologies

TL;DR

This paper explores the constraints on matter configurations in Randall-Sundrum cosmologies, revealing that only a stiff fluid equation of state is compatible with static bulk solutions and analyzing resulting brane cosmologies.

Contribution

It demonstrates that realistic brane matter cannot exist in static two-brane setups and identifies the unique stiff fluid equation of state compatible with static bulk configurations.

Findings

No realistic brane matter in static two-brane models.

Only a stiff fluid ($p=\rho$) is allowed for bulk matter.

Derived brane cosmologies resemble Friedmann-Robertson-Walker models.

Abstract

We investigate constraints for including bulk and brane matter in the Randall- Sundrum model. In static configurations with two zero thickness branes, we find that no realistic brane matter is possible. We also consider the possibility that the radion has stabilized by dissipating its energy into the bulk in the form of some unspecified matter, and find the Randall-Sundrum cosmological solutions in the presence of bulk ideal fluid. We discover that the metric is necessarily in a static configuration. We also discover that there is only one allowed equation of state for the bulk fluid, $p=\rho $, corresponding to the stiff ideal fluid. We find the corresponding brane cosmologies and compare them with the Friedmann-Robertson-Walker model.