String field theory in curved spacetime and the resolution of spacelike singularities

Abstract

We attempt to understand the fate of spacelike gravitational singularities in string theory via the quantum stress tensor for string matter in a fixed background. We first approximate the singularity with a homogeneous anisotropic background and review the minisuperspace equations describing the evolution of the scale factors and the dilaton. We then review and discuss the behavior of large strings in such models. In a simple model which expands isotropically for a finite period of time we compute the number density of strings produced by quantum pair production and find that this number, and thus the stress tensor, becomes infinite when the Hubble volume of the expansion exceeds the string scale, in a manner reminiscent of the Hagedorn transition. Based on this calculation we argue that either the region near the singularity undergoes a phase transition when the density reaches the order of a string mass per string volume, or that the backreaction of the produced string matter dramatically modifies the geometry.

Some minor errors corrected; version to be published in Class. Quant. Grav.; standard LaTeX, uses epsf.tex, 44 pages, 4 figures

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