The primordial curvature perturbation in the ekpyrotic Universe

TL;DR

The paper critically reevaluates the generation of the primordial curvature perturbation in the ekpyrotic Universe by including gravitational back-reaction. It finds that the spectrum during collapse becomes strongly scale-dependent and is greatly suppressed when metric perturbations are accounted for, in contrast to earlier results that ignored back-reaction and predicted a flat spectrum. The analysis argues that, even with a smooth bounce, achieving a scale-invariant spectrum requires non-adiabatic pressure or additional modifications, making the ekpyrotic/pre-big-bang scenarios less favorable than inflation for structure formation. A brief note suggests that simple potential modifications that mimic inflation could salvage viable perturbations in an alternative scenario.

Abstract

In the ekpyrotic scenario the Universe is initially collapsing, the energy density coming from a scalar field with a negative exponential potential. On the basis of a calculation ignoring the gravitational back-reaction the authors of the scenario claim that during collapse the vacuum fluctuation creates a perturbation in the comoving curvature, which has a flat spectrum in accordance with observation. In this note the back-reaction is included, and it is found that the spectrum during collapse is strongly scale-dependent with negligible magnitude. The spectrum is continuous across the bounce if the spacetime is smooth, making it unlikely that the ekpyrotic scenario can be compatible with observation.