Passing through the bounce in the ekpyrotic models

TL;DR

This paper critically examines the ekpyrotic scenario's assumptions, especially the perturbation passing prescription, demonstrating limitations in reproducing exact results and the non-instantaneous nature of bounces in Einstein gravity.

Contribution

It provides an exact model analysis of the ekpyrotic bounce, highlighting issues with the perturbation prescription and the non-viability of arbitrarily short bounces in Einstein gravity.

Findings

The new ekpyrotic prescription depends on a non-physical normalization.

It fails to reproduce exact results for sharp transitions.

Bounces in Einstein gravity cannot be arbitrarily short.

Abstract

By considering a simplified but exact model for realizing the ekpyrotic scenario, we clarify various assumptions that have been used in the literature. In particular, we discuss the new ekpyrotic prescription for passing the perturbations through the singularity which we show to provide a spectrum depending on a non physical normalization function. We also show that this prescription does not reproduce the exact result for a sharp transition. Then, more generally, we demonstrate that, in the only case where a bounce can be obtained in Einstein General Relativity without facing singularities and/or violation of the standard energy conditions, the bounce cannot be made arbitrarily short. This contrasts with the standard (inflationary) situation where the transition between two eras with different values of the equation of state can be considered as instantaneous. We then argue that the usually conserved quantities are not constant on a typical bounce time scale. Finally, we also examine the case of a test scalar field (or gravitational waves) where similar results are obtained. We conclude that the full dynamical equations of the underlying theory should be solved in a non singular case before any conclusion can be drawn.