Brane gases in the early universe: thermodynamics and cosmology

TL;DR

This paper explores the thermodynamics and cosmological implications of brane gases in the early universe within M-theory, analyzing their role in dimensional decompactification and the conditions affecting brane annihilation.

Contribution

It introduces a detailed thermodynamic model of brane gases, estimates the Hagedorn temperature, and numerically investigates how brane dynamics influence the universe's dimensional structure.

Findings

Brane gases can lead to decompactification of three spatial dimensions.

Most branes annihilate before freeze-out for typical initial volumes.

The initial volume constraints are consistent with holographic bounds.

Abstract

We consider the thermodynamic and cosmological properties of brane gases in the early universe. Working in the low energy limit of M-theory we assume the universe is a homogeneous but anisotropic 10-torus containing wrapped 2-branes and a supergravity gas. We describe the thermodynamics of this system and estimate a Hagedorn temperature associated with excitations on the branes. We investigate the cross-section for production of branes from the thermal bath and derive Boltzmann equations governing the number of wrapped branes. A brane gas may lead to decompactification of three spatial dimensions. To investigate this possibility we adopt initial conditions in which we fix the volume of the torus but otherwise assume all states are equally likely. We solve the Einstein-Boltzmann equations numerically, to determine the number of dimensions with no wrapped branes at late times; these unwrapped dimensions are expected to decompactify. Finally we consider holographic bounds on the initial volume, and find that for allowed initial volumes all branes typically annihilate before freeze-out can occur.