Primordial perturbations and non-Gaussianities in Hořava-Lifshitz gravity

TL;DR

Hořava-Lifshitz gravity provides a renormalizable framework with UV anisotropic scaling that makes primordial scalar perturbations scale-invariant in the ultraviolet, reducing the need for exponential expansion or slow-roll. The authors derive the full second-order perturbation action and compute the bispectrum, finding equilateral non-Gaussianity of order unity and locally suppressed non-Gaussianity, thereby offering a new constraint on HL gravity. This work suggests HL gravity can reproduce certain inflationary phenomenology without standard dynamics and motivates studying full metric perturbations and alternative kinetic terms. Overall, the results illuminate how UV HL dynamics shape primordial fluctuations and their observational signatures.

Abstract

We investigate primordial perturbations and non-gaussianities in the Hořava-Lifshitz theory of gravitation. In the UV limit, the scalar perturbation in the Hořava 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 Hořava-Lifshitz gravity.