  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 an FRW phase. The models also
provide a quantitative testing ground for ideas about the origin of inflation,
such as the various `no-boundary/tunnelling' proposals, and the
`eternal/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.
