Singularities in and Stability of Ooguri-Vafa-Verlinde Cosmologies

Abstract

Ooguri, Vafa, and Verlinde have recently proposed an approach to string cosmology which is based on the idea that cosmological string moduli should be selected by a Hartle-Hawking wave function. They are led to consider a certain Euclidean space which has *two different Lorentzian interpretations*, one of which is a model of an *accelerating cosmology*. We describe in detail how to implement this idea without resorting to a "complex metric". We show that the four-dimensional version of the OVV cosmology is null geodesically incomplete but has no curvature singularity; also that it is [barely] stable against the Seiberg-Witten process [nucleation of brane pairs]. The introduction of matter satisfying the Null Energy Condition has the paradoxical effect of both stabilizing the spacetime and rendering it genuinely singular. We show however that it is possible to arrange for an effective violation of the NEC in such a way that the singularity is avoided and yet the spacetime remains stable. The possible implications for the early history of these cosmologies are discussed.