  We introduce "anamorphic" cosmology, an approach for explaining the
smoothness and flatness of the universe on large scales and the generation of a
nearly scale-invariant spectrum of adiabatic density perturbations. The
defining feature is a smoothing phase that acts like a contracting universe
based on some Weyl frame-invariant criteria and an expanding universe based on
other frame-invariant criteria. An advantage of the contracting aspects is that
it is possible to avoid the multiverse and measure problems that arise in
inflationary models. Unlike ekpyrotic models, anamorphic models can be
constructed using only a single field and can generate a nearly scale-invariant
spectrum of tensor perturbations. Anamorphic models also differ from pre-big
bang and matter bounce models that do not explain the smoothness. We present
some examples of cosmological models that incorporate an anamorphic smoothing
phase.
