Ekpyrotic loop quantum cosmology

TL;DR

This paper explores how loop quantum cosmology modifies the ekpyrotic universe model, resolving singularities and enabling detailed analysis of scalar perturbations through a quantum bounce, with implications for observable cosmological spectra.

Contribution

It demonstrates the evolution of scalar perturbations in ekpyrotic models within loop quantum cosmology, showing nearly scale-invariant spectra for two-field scenarios.

Findings

Single scalar field yields a blue spectrum post-bounce.

Two scalar fields produce a nearly scale-invariant spectrum.

Quantum bounce connects contracting and expanding phases smoothly.

Abstract

We consider the ekpyrotic paradigm in the context of loop quantum cosmology. In loop quantum cosmology the classical big-bang singularity is resolved due to quantum gravity effects, and so the contracting ekpyrotic branch of the universe and its later expanding phase are connected by a smooth bounce. Thus, it is possible to explicitly determine the evolution of scalar perturbations, from the contracting ekpyrotic phase through the bounce and to the post-bounce expanding epoch. The possibilities of having either one or two scalar fields have been suggested for the ekpyrotic universe, and both cases will be considered here. In the case of a single scalar field, the constant mode of the curvature perturbations after the bounce is found to have a blue spectrum. On the other hand, for the two scalar field ekpyrotic model where scale-invariant entropy perturbations source additional terms in the curvature perturbations, the power spectrum in the post-bounce expanding cosmology is shown to be nearly scale-invariant and so agrees with observations.