Adiabatic ekpyrosis: Scale-invariant curvature perturbations from a single scalar field in a contracting universe

The Universe can be made flat and smooth by undergoing a phase of ultraslow (ekpyrotic) contraction, a condition achievable with a single, canonical scalar field and conventional general relativity. It has been argued, though, that generating scale-invariant density perturbations requires at least two scalar fields and a two-step process that first produces entropy fluctuations and then converts them to curvature perturbations. In this Letter we identify a loophole in the argument and introduce an ekpyrotic model based on a single, canonical scalar field that generates nearly scale-invariant curvature fluctuations through a purely "adiabatic mechanism" in which the background evolution is a dynamical attractor. The resulting spectrum can be slightly red with distinctive non-Gaussian fluctuations.