The tachyon at the end of the universe

We show that a tachyon condensate phase replaces the spacelike singularity incertain cosmological and black hole spacetimes in string theory. We analyzeexplicitly a set of examples with flat spatial slices in various dimensionswhich have a winding tachyon condensate, using worldsheet path integral methodsfrom Liouville theory. In a vacuum with no excitations above the tachyonbackground in the would-be singular region, we analyze the production of closedstrings in the resulting state in the bulk of spacetime. We find a thermalresult reminiscent of the Hartle-Hawking state, with tunably small energydensity. The amplitudes exhibit a self-consistent truncation of support to theweakly-coupled small-tachyon region of spacetime. We argue that the backgroundis accordingly robust against back reaction, and that the resulting stringtheory amplitudes are perturbatively finite, indicating a resolution of thesingularity and a mechanism to start or end time in string theory. Finally, wediscuss the generalization of these methods to examples with positively curvedspatial slices.Comment: 33 pages, 1 eps figure; v2: clarifications, added ref