Fluctuations in a Ho\v{r}ava-Lifshitz Bouncing Cosmology

TL;DR

This paper investigates linear cosmological perturbations in Hořava-Lifshitz gravity with spatial curvature, demonstrating non-singular evolution through a bounce and showing it can produce scale-invariant fluctuations consistent with the matter bounce scenario.

Contribution

It extends the analysis of perturbations in Hořava-Lifshitz gravity to include spatial curvature, confirming the absence of extra degrees of freedom and viability for structure formation.

Findings

Perturbations remain non-singular through the bounce.

Scale-invariant fluctuations are produced in a matter-dominated contracting phase.

No extra dynamical degrees of freedom for scalar perturbations.

Abstract

Ho\v{r}ava-Lifshitz gravity is a potentially UV complete theory with important implications for the very early universe. In particular, in the presence of spatial curvature it is possible to obtain a non-singular bouncing cosmology. The bounce is realized as a consequence of higher order spatial curvature terms in the gravitational action. Here, we extend the study of linear cosmological perturbations in Ho\v{r}ava-Lifshitz gravity coupled to matter in the case when spatial curvature is present. As in the case without spatial curvature, we find that there is no extra dynamical degree of freedom for scalar metric perturbations. We study the evolution of fluctuations through the bounce and show that the solutions remain non-singular throughout. If we start with quantum vacuum fluctuations on sub-Hubble scales in the contracting phase, and if the contracting phase is dominated by pressure-less matter, then for $\lambda = 1$ and in the infrared limit the perturbations at late times are scale invariant. Thus, Ho\v{r}ava-Lifshitz gravity can provide a realization of the ``matter bounce'' scenario of structure formation.