Inflationary perturbations with Lifshitz scaling

TL;DR

This paper explores how Lifshitz scaling in Hořava-Lifshitz gravity affects inflationary perturbations, showing that in the non-projectable version, the curvature perturbation remains conserved and exhibits distinctive signatures in the power spectrum.

Contribution

It demonstrates that in non-projectable HL gravity, the adiabatic perturbation remains conserved due to the decoupling of the khronon, and identifies potential observational signatures of Lorentz violation.

Findings

Adiabatic perturbation spectrum is conserved in non-projectable HL gravity.

Lifshitz scaling modifies the dispersion relation of inflaton perturbations.

Violation of the consistency relation between tensor-to-scalar ratio and spectral tilt.

Abstract

Instead of Lorentz invariance, gravitational degrees of freedom may obey Lifshitz scaling at high energies, as it happens in Ho\v{r}ava's proposal for quantum gravity. We study consequences of this proposal for the spectra of primordial perturbations generated at inflation. Breaking of 4D diffeomorphism (Diff) invariance down to the foliation-preserving Diff in Ho\v{r}ava-Lifshitz (HL) gravity leads to appearance of a scalar degree of freedom in the gravity sector, khronon, which describes dynamics of the time foliation. One can naively expect that mixing between inflaton and khronon will jeopardize conservation of adiabatic perturbations at super Hubble scales. This indeed happens in the projectable version of the theory. By contrast, we find that in the non-projectable version of HL gravity, khronon acquires an effective mass which is much larger than the Hubble scale well before the Hubble crossing time and decouples from the adiabatic curvature perturbation $\zeta$ sourced by the inflaton fluctuations. As a result, at super Hubble scales the adiabatic perturbation $\zeta$ behaves as in an effectively single field system and its spectrum is conserved in time. Lifshitz scaling is imprinted in the power spectrum of $\zeta$ through the modified dispersion relation of the inflaton. We point out violation of the consistency relation between the tensor-to-scalar ratio and the spectral tilt of primordial gravitational waves and suggest that it can provide a signal of Lorentz violation in inflationary era.