Singularities in Kaluza-Klein-Friedmann cosmological models.

Abstract

We consider five-dimensional Kaluza-Klein cosmologies that have three-dimensional spatial sections corresponding to Friedmann (Robertson-Walker) spaces. The extra (flat) dimension can be identified to close it to a circle. We investigate the ``crack-of-doom'' singularity in which the extra dimension goes to zero size, inducing a five-dimensional singularity of which the embedded four-dimensional cosmology has no indication until the singularity. In the Chodos-Detweiler model this crack-of-doom singularity occurs at time =\ensuremath{\infty}, while in a closed Friedmann model like those of Mezzacappa and Matzner, it occurs at a finite time near the maximum of expansion. We present a diagrammatic solution for a range of such models, and show that by appropriate (parameter) choices, the ``crack of doom'' can be avoided both in three-sphere and in three-hyperboloid Kaluza-Klein-Friedmann solutions.