On Cosmological String Backgrounds with Toroidal Isometries

A large class of cosmological solutions (of the Einstein equations) in string theory, in the presence of Maxwell fields, is obtained by $O(d,d)$ transformations of simple backgrounds with $d$ toroidal isometries. In all the examples in which we find a (closed) expanding universe, such that the universe admits a smooth, complete initial value hypersurface, a naked singularity may form only at the time when the universe collapses. The discrete symmetry group $O(d,d,Z)$ identifies different cosmological solutions with a background corresponding to a (relatively) simple CFT, and therefore, may be useful in understanding the properties of naked singularities in string theory.