The failure of cosmological perturbation theory in the new ekpyrotic scenario

Cosmological perturbation theory fails in the new ekpyrotic scenario before the scale factor of the Universe reaches zero. As a result, the scenario does not provide a mechanism for generating the observed curvature perturbation at the bounce. Introduction It is now clear that the dominant cause of large-scale structure in the Universe is a perturbation in the spatial curvature [1]. The perturbation exists already when cosmological scales are approaching horizon entry, at which stage it has an almost flat spectrum. It presumably originates during an early era of superluminal evolution, defined as one in which comoving scales are leaving the horizon, at the beginning of which the entire observable Universe is inside the horizon. During superluminal evolution the curvature of the Universe in Hubble units is decreasing, explaining naturally the near-flatness of the observable Universe. The usual hypothesis concerning the superluminal era is that it is one of expansion, or in other words an era of inflation, with slowly varying Hubble parameter H . During inflation, each canonically-normalized light scalar field acquires a perturbation with a flat spectrum, and this provides a natural origin for the observed curvature perturbation. The curvature perturbation might be generated directly during inflation from the perturbation in the slowly-rolling inflaton field [1], or indirectly [2] by a different field (curvaton) whose isocurvature density perturbation is converted into a curvature perturbation during some radiation-dominated era after inflation. The alternative to inflation is an era of superluminal collapse (negative Hubble parameter) giving way at some stage to expansion (positive Hubble parameter). The theory describing the bounce cannot be standard field theory with Einstein gravity, corresponding to an action of the form