Variations on Kaluza-Klein Cosmology

TL;DR

This paper explores how compactified extra dimensions influence the universe's thermal history and discusses connections with non-critical string cosmology, showing that topology affects thermal evolution but not the overall dynamics.

Contribution

It demonstrates that topological effects do not alter the universe's equation of state but do impact its thermal history, linking quantum fields in compactified spaces to string-inspired cosmology.

Findings

Equation of state remains unchanged by topology.

Thermal history depends on non-trivial topology.

Links between string cosmology and hot massless fields are discussed.

Abstract

We investigate the cosmological consequences of having quantum fields living in a space with compactified dimensions. We will show that the equation of state is not modified by topological effects and so the dynamics of the universe remains as it is in the infinite volume limit. On the contrary the thermal history of the universe depends on terms that are associated with having non-trivial topology. In the conclusions we discuss some issues about the relationship between the $c=1$ non-critical string-inspired cosmology and the result obtained with matter given by a hot massless field in $S^{1}\times \mbox{\bf R}$.