String Propagation in the Presence of Cosmological Singularities

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Abstract
We study string propagation in a spacetime with positive cosmological constant, which includes a circle whose radius approaches a finite value as |t|\to\infty, and goes to zero at t=0. Near this cosmological singularity, the spacetime looks like R^{1,1}/Z. In string theory, this spacetime must be extended by including four additional regions, two of which are compact. The other two introduce new asymptotic regions, corresponding to early and late times, respectively. States of quantum fields in this spacetime are defined in the tensor product of the two Hilbert spaces corresponding to the early time asymptotic regions, and the S-matrix describes the evolution of such states to states in the tensor product of the two late time asymptotic regions. We show that string theory provides a unique continuation of wavefunctions past the cosmological singularity, and allows one to compute the S-matrix. The incoming vacuum evolves into an outgoing state with particles. We also discuss instabilities of this cosmological spacetime, and the question of holography in this space. Finally, we briefly comment on the relation of our results to recent discussions of de Sitter space.

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