Scale-invariant perturbations in ekpyrotic cosmologies without fine-tuning of initial conditions

TL;DR

This paper presents a counterexample in ekpyrotic cosmologies where scale-invariant entropic perturbations are generated without fine-tuning initial conditions, challenging previous assumptions about instability requirements.

Contribution

The paper introduces a simple model that produces scale-invariant entropic perturbations during ekpyrotic contraction without initial condition fine-tuning.

Findings

A Gaussian, scale-invariant spectrum of entropic perturbations is achievable without fine-tuning.

The model challenges previous views on the instability requirement for scale invariance.

Generalizations of the model are discussed.

Abstract

Ekpyrotic bouncing cosmologies have been proposed as alternatives to inflation. In these scenarios, the universe is smoothed and flattened during a period of slow contraction preceding the bounce while quantum fluctuations generate nearly scale-invariant super-horizon perturbations that seed structure in the post-bounce universe. An analysis by Tolley and Wesley (2007) showed that, for a wide range of ekpyrotic models, generating a scale-invariant spectrum of adiabatic or entropic fluctuations is only possible if the cosmological background is unstable, in which case the scenario is highly sensitive to initial conditions. In this paper, we analyze an important counterexample: a simple action that generates a Gaussian, scale-invariant spectrum of entropic perturbations during ekpyrotic contraction without requiring fine-tuned initial conditions. Based on this example, we discuss some generalizations.