The b-completion of the Friedmann space

Abstract

We study the b-completion of the three Friedmann models of the Universe, having as models for 3-space the sphere, the Euclidean space or the hyperbolic space. We show that in the first case there is just one singularity, having the full completion as only neighborhood. In the other two cases there is one essential singularity, which is the limit of all past causal geodesics; again, it has a single neighborhood. This extends results by Bosshard [On the b-boundary of the closed Friendmann Model, Commun. Math. Phys. 46 (1976) 263-268] and Johnson [The bundle boundary in some special cases, J. Math. Phys. 18 (5) (1977) 898-902] on the closed Friedmann model. (C) 1999 Elsevier Science B.V. All rights reserved.