The Geometrization of Matter Proposal in the Barrett-Crane Model and Resolution of Cosmological Problems

The Barrett-Crane model [?] [?] is a constrained topological state sum model for quantum gravity. Recently [?] it was proposed that this model might incorporate matter and gauge interactions if the condition on triangulations to be manifolds were relaxed. That is, conical singularities would act as seeds of matter in the quantum geometry of the state sum. The purpose of this paper is to examine the consequences of this proposal, and of spin foam models in general, for early universe phenomenology. We feel that although the BC model, and the conical matter proposal in particular, are not yet sufficiently well understood, the connections are provocative. Conversely, one would like to use cosmology as a guiding principle for developing experimental techniques in spin foam models that could be used to explain and predict real observations. The point of this paper is that natural approximations motivated by the conical matter proposal (CMP) seem to shed light on the full range of puzzles of the early universe. Although each argument is in need of further substantiation, the overall picture seems striking in itself. To clarify this point, and since the communities of researchers in spin foam models and early universe phenomenology are not generally aware of each other’s work, this paper begins with a self contained introduction to the range of early universe phenomenological issues. We then give a nontechnical introduction to the categorical state sum program and the BC model in particular, together with the conical matter proposal. We conclude with a discussion of a range of phenomenological problems which have plausible solutions in the state sum picture. Although we have tried to make the paper accessible to cosmologists by giving physical explanations for the state sum models as far as possible, they do make use of branches of mathematics not generally familiar to physicists, so interested readers are strongly recommended to consult the references. We believe that the current form of the model is likely to be less important than the fact that it leads to calculations that probe poorly understood phenomena.