Primordial perturbations and non-Gaussianities in Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper explores how Hořava-Lifshitz gravity affects primordial perturbations and non-Gaussianities, revealing that scale-invariance arises naturally and that certain non-Gaussian features could be significantly larger than in standard inflation.

Contribution

It demonstrates that in Hořava-Lifshitz gravity, primordial scalar perturbations are naturally scale-invariant in the UV limit, allowing relaxation of inflation conditions and predicting potentially large non-Gaussianities.

Findings

Scalar perturbations are scale-invariant in the UV limit.

Equilateral non-Gaussianity is of order unity.

Local non-Gaussianity remains small, similar to standard models.

Abstract

We investigate primordial perturbations and non-gaussianities in the Ho\v{r}ava-Lifshitz theory of gravitation. In the UV limit, the scalar perturbation in the Ho\v{r}ava theory is naturally scale-invariant, ignoring the details of the expansion of the Universe. One may thus relax the exponential inflation and the slow-roll conditions for the inflaton field. As a result, it is possible that the primordial non-gaussianities, which are ``slow-roll suppressed'' in the standard scenarios, become large. We calculate the non-gaussianities from the bispectrum of the perturbation and find that the equilateral-type non-gaussianity is of the order of unity, while the local-type non-gaussianity remains small, as in the usual single-field slow-roll inflation model in general relativity. Our result is a new constraint on the the Ho\v{r}ava-Lifshitz gravity.