The uninvited guest in mixed derivative Ho\v{r}ava Gravity

TL;DR

This paper analyzes a modified version of Hořava gravity with mixed derivatives, revealing an additional unstable scalar mode that challenges the theory's consistency and the suppression of Lorentz violation.

Contribution

It provides a detailed calculation of the propagating modes in the minimal mixed derivative Hořava gravity, identifying an extra scalar graviton and its instability.

Findings

The theory has four propagating degrees of freedom.

An additional scalar graviton mode is present.

The new scalar mode is unstable at low energies.

Abstract

We revisit the mixed derivative extension of Ho\v{r}ava gravity which was designed to address the naturalness problems of the standard theory in the presence of matter couplings. We consider the minimal theory with mixed derivative terms that contain two spatial and two temporal derivatives. Including all terms compatible with the (modified) scaling rules and the foliation preserving diffeomorphisms, we calculate the dispersion relations of propagating modes. We find that the theory contains four propagating degrees of freedom, as opposed to three in the standard Ho\v{r}ava gravity. The new degree of freedom is another scalar graviton and it is unstable at low energies. Our result brings tension to the Lorentz violation suppression mechanism that relies on separation of scales.