The Tachyon at the End of the Universe

We show that a tachyon condensate phase replaces the spacelike singularity in certain cosmological and black hole spacetimes in string theory. We analyze explicitly a set of examples with flat spatial slices in various dimensions which have a winding tachyon condensate, using worldsheet path integral methods from Liouville theory. In a vacuum with no excitations above the tachyon background in the would-be singular region, we analyze the production of closed strings in the resulting state in the bulk of spacetime. We find a thermal result reminiscent of the Hartle-Hawking state, with tunably small energy density. The amplitudes exhibit a self-consistent truncation of support to the weakly-coupled small-tachyon region of spacetime. We argue that the background is accordingly robust against back reaction, and that the resulting string theory amplitudes are perturbatively finite, indicating a resolution of the singularity and a mechanism to start or end time in string theory. Finally, we discuss the generalization of these methods to examples with positively curved spatial slices.