Closed string tachyon condensation and worldsheet inflation

Closed string tachyon condensation in spacetime generates potentials on the worldsheet that model two-dimensional inflationary cosmology. These models illustrate and elucidate a variety of aspects of inflation, in particular the generation of quantum fluctuations and their back reaction on geometry. We exhibit a class of Liouville gravity models coupled to matter that can exhibit, for example, (a) pure de Sitter gravity, (b) slow-roll inflation, (c) topological inflation, and (d) graceful exit into a Friedmann-Robertson-Walker (FRW) phase. The models also provide a quantitative testing ground for ideas about the origin of inflation, such as the various ``no-boundary or tunnelling'' proposals, and the ``eternal or chaotic'' inflationary scenario. We suggest an alternative mechanism for quantum creation of cosmological spacetimes which, in the context of the model, provides a natural explanation for why the typical FRW cosmology at large scales underwent a period of inflation at small scale.