Adiabatic Ekpyrosis: Scale-Invariant Curvature Perturbations from a Single Scalar Field in a Contracting Universe

Abstract

The universe can be made flat and smooth by undergoing a phase of ultra-slow (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 paper, 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.

5 pages. v2: Minor corrections. v3: Expanded discussion of attractor property, included numerical work confirming scale invariance, improved notation, and added references