On Stability of Asymptotically Free Mimetic Ho\v{r}ava Gravity

TL;DR

This paper analyzes the linear stability of cosmological perturbations in asymptotically free mimetic Hořava gravity, showing that higher order spatial curvature terms can stabilize scalar perturbations but may affect primordial spectra.

Contribution

It demonstrates that adding Hořava-like higher order spatial curvature terms stabilizes scalar perturbations in mimetic gravity models.

Findings

Higher order curvature terms lift gradient instability.

Primordial spectra are altered by varying sound speed.

Exponential expansion with graceful exit is a generic feature.

Abstract

Asymptotically free mimetic gravity has been introduced as a proposal for a classical limiting curvature theory with the purpose of singularity resolution. It was found that in a spatially flat universe an initial stage of exponential expansion with graceful exit is a generic consequence, regardless of the matter content. In this work I will analyze linear stability of cosmological perturbations in such a model, considering only the degrees of freedom of pure mimetic gravity. I show that the addition of Ho\v{r}ava-gravity-like higher order spatial curvature terms can lift the gradient instability of scalar perturbations, even when the gradient term has the wrong sign throughout. Calculating the primordial spectra of tensor and scalar perturbations in the simplest single component model, I find that the initially scale invariant spectra turn out to be destroyed later by the rapidly varying speed of sound at horizon exit.