Nature of the singularity in some Brans-Dicke universes

Abstract

In the background of somewhat conflicting results about the possibility of nonsingular cosmological solutions of the Brans-Dicke equations, this article investigates some explicit solutions of these equations. It is found that, in the solutions presented, the material energy densit never becomes infinite-either the spatial volume collapses or the gravitational 'constant' shows singular behaviour according as one adopts one or the other of the two units discussed by Dicke. While such situations are obtained with the equation of state p=ερ (ε=a constant ≠1/3), the constant ω in Brans-Dicke equations has to be given a negative value contrary to observational requirement.