Quantum propagation across cosmological singularities
  The initial singularity is the most troubling feature of the standard
cosmology, which quantum effects are hoped to resolve. In this paper, we study
quantum cosmology with conformal (Weyl) invariant matter. We show it is natural
to extend the scale factor to negative values, allowing a large, collapsing
Universe to evolve across a quantum "bounce" into an expanding Universe like
ours. We compute the Feynman propagator for Friedmann-Robertson-Walker
backgrounds exactly, identifying curious pathologies in the case of curved
(open or closed) universes. We then include anisotropies, fixing the operator
ordering of the quantum Hamiltonian by imposing covariance under field
redefinitions and again finding exact solutions. We show how complex classical
solutions allow one to circumvent the singularity while maintaining the
validity of the semiclassical approximation. The simplest isotropic universes
sit on a critical boundary, beyond which there is qualitatively different
behavior, with potential for instability. Additional scalars improve the
theory's stability. Finally, we study the semiclassical propagation of
inhomogeneous perturbations about the flat, isotropic case, at linear and
nonlinear order, showing that, at least at this level, there is no particle
production across the bounce. These results form the basis for a promising new
approach to quantum cosmology and the resolution of the big bang singularity.
