Towards a Cosmological Dual to Inflation
  We derive all single-field cosmologies with unit sound speed that generate
scale invariant curvature perturbations on a dynamical attractor background. We
identify three distinct phases: slow-roll inflation; a slowly contracting
adiabatic ekpyrotic phase, described by a rapidly-varying equation of state;
and a novel adiabatic ekpyrotic phase on a slowly expanding background. All of
these yield identical power spectra. The degeneracy is broken at the 3-point
level: unlike the nearly gaussian spectrum of slow-roll inflation, adiabatic
ekpyrosis predicts large non-gaussianities on small scales.
