On the stability of the primordial closed string gas

TL;DR

This paper analyzes the thermodynamics of a high-energy closed string gas in a toroidal space, comparing different regularizations and ensemble descriptions, with implications for string cosmology and the Hagedorn transition.

Contribution

It provides a new regularization approach to study the specific heat and thermodynamic behavior of a closed string gas, contrasting with previous Brandenberger-Vafa calculations.

Findings

Microcanonical analysis challenges previous specific heat results.

Complex temperature formalism reveals consistent analytic structure at the Hagedorn singularity.

Different regularizations yield comparable thermodynamic features.

Abstract

We recast the study of a closed string gas in a toroidal container in the physical situation in which the single string density of states is independent of the volume because energy density is very high. This includes the gas for the well known Brandenberger-Vafa cosmological scenario. We describe the gas in the grandcanonical and microcanonical ensembles. In the microcanonical description, we find a result that clearly confronts the Brandenberger-Vafa calculation to get the specific heat of the system. The important point is that we use the same approach to the problem but a different regularization. By the way, we show that, in the complex temperature formalism, at the Hagedorn singularity, the analytic structure obtained from the so-called F-representation of the free energy coincides with the one computed using the S-representation.