Large Radius Hagedorn Regime in String Gas Cosmology

TL;DR

This paper analyzes the high-density regime of string gases in a large universe, deriving the equation of state and cosmological evolution, revealing a non-vanishing pressure and an exponentially growing Hagedorn phase duration.

Contribution

It provides the first detailed calculation of the equation of state and cosmological dynamics in the large radius Hagedorn regime of string gas cosmology, improving upon previous approximations.

Findings

Pressure is of order one in the regime.

Hagedorn phase duration grows exponentially with entropy.

Solutions differ significantly from earlier approximate models.

Abstract

We calculate the equation of state of a gas of strings at high density in a large toroidal universe, and use it to determine the cosmological evolution of background metric and dilaton fields in the entire large radius Hagedorn regime, (ln S)^{1/d} << R << S^{1/d} (with S the total entropy). The pressure in this regime is not vanishing but of O(1), while the equation of state is proportional to volume, which makes our solutions significantly different from previously published approximate solutions. For example, we are able to calculate the duration of the high-density "Hagedorn" phase, which increases exponentially with increasing entropy, S. We go on to discuss the difficulties of the scenario, quantifying the problems of establishing thermal equilibrium and producing a large but not too weakly-coupled universe.