Primordial Perturbation in Horava-Lifshitz Cosmology

TL;DR

This paper investigates how primordial perturbations can be generated in Horava-Lifshitz cosmology, showing that scale-invariant spectra are possible in various early universe expansions, but require specific conditions for observability.

Contribution

It validates that scale-invariant primordial perturbations can arise in Horava-Lifshitz cosmology for a broad class of expansion histories, extending previous understanding.

Findings

Scale-invariant perturbations can be generated for a> t^n with n>1/3.

For observable universe perturbations, n>1 is generally required.

The UV scale must be low for certain expansion scenarios to produce observable perturbations.

Abstract

Recently, Ho\v{r}ava has proposed a renormalizable theory of gravity with critical exponent z=3 in the UV. This proposal might imply the scale invariant primordial perturbation can be generated in any expansion of early universe with a\sim t^n and n>1/3, which, in this note, will be validated by solving the motion equation of perturbation mode on super sound horizon scale for any background evolution of early universe. However, it is found that it seems that if we require the efolding number of primordial perturbation is suitable for observable universe, n>1 still need to be satisfied, unless the scale of UV regime is quite low.