Universality Class in Conformal Inflation
  We develop a new class of chaotic inflation models with spontaneously broken
conformal invariance. Observational consequences of a broad class of such
models are stable with respect to strong deformations of the scalar potential.
This universality is a critical phenomenon near the point of enhanced symmetry,
SO(1,1), in case of conformal inflation. It appears because of the exponential
stretching of the moduli space and the resulting exponential flattening of
scalar potentials upon switching from the Jordan frame to the Einstein frame in
this class of models. This result resembles stretching and flattening of
inhomogeneities during inflationary expansion. It has a simple interpretation
in terms of velocity versus rapidity near the Kahler cone in the moduli space,
similar to the light cone of special theory of relativity. This effect makes
inflation possible even in the models with very steep potentials. We describe
conformal and superconformal versions of this cosmological attractor mechanism.
