Modeling Quantum Gravity Effects in Inflation
  Cosmological models in 1+1 dimensions are an ideal setting for investigating
the quantum structure of inflationary dynamics -- gravity is renormalizable,
while there is room for spatial structure not present in the minisuperspace
approximation. We use this fortuitous convergence to investigate the mechanism
of slow-roll eternal inflation. A variant of 1+1 Liouville gravity coupled to
matter is shown to model precisely the scalar sector of cosmological
perturbations in 3+1 dimensions. A particular example of quintessence in 1+1d
is argued on the one hand to exhibit slow-roll eternal inflation according to
standard criteria; on the other hand, a field redefinition relates the model to
pure de Sitter gravity coupled to a free scalar matter field with no potential.
This and other examples show that the standard logic leading to slow-roll
eternal inflation is not invariant under field redefinitions, thus raising
concerns regarding its validity. Aspects of the quantization of Liouville
gravity as a model of quantum de Sitter space are also discussed.
