For models of dilaton-gravity with a possible exponential potential, such as
the tensor-scalar sector of IIA supergravity, we show how cosmological
solutions correspond to trajectories in a 2D Milne space (parametrized by the
dilaton and the scale factor). Cosmological singularities correspond to points
at which a trajectory meets the Milne horizon, but the trajectories can be
smoothly continued through the horizon to an instanton solution of the
Euclidean theory. We find some exact cosmology/instanton solutions that lift to
black holes in one higher dimension. For one such solution, the singularities
of a big crunch to big bang transition mediated by an instanton phase lift to
the black hole and cosmological horizons of de Sitter Schwarzschild spacetimes.Comment: 24 pages, 2 figure