Cosmological string models from Milne spaces and SL(2,Z) orbifold

TL;DR

This paper constructs four-dimensional cosmological string models using Milne universes with extra dimensions, explores SL(2,Z) orbifold identifications, and analyzes the string spectrum and wave functions near singularities.

Contribution

It introduces new cosmological string models based on Milne spaces and SL(2,Z) orbifolds, linking them to null orbifolds and analyzing their spectra.

Findings

Bound for the energy gap derived from harmonic functions.

Infinite number of string excitations with finite degeneracy.

Physical winding states become light near singularities.

Abstract

The $n+1$-dimensional Milne Universe with extra free directions is used to construct simple FRW cosmological string models in four dimensions, describing expansion in the presence of matter with $p=k \rho $, $k=(4-n)/3n$. We then consider the n=2 case and make SL(2,Z) orbifold identifications. The model is surprisingly related to the null orbifold with an extra reflection generator. The study of the string spectrum involves the theory of harmonic functions in the fundamental domain of SL(2,Z). In particular, from this theory one can deduce a bound for the energy gap and the fact that there are an infinite number of excitations with a finite degeneracy. We discuss the structure of wave functions and give examples of physical winding states becoming light near the singularity.