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

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 $p=k ρ$, $k=(4-n)/3n$. 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.