Spatially covariant gravity: Degeneracy condition and mimetic formulation

TL;DR

This paper analyzes spatially covariant gravity theories, showing how degeneracy conditions reduce scalar degrees of freedom and exploring their cosmological perturbations, especially in mimetic gravity contexts.

Contribution

It provides a perturbative analysis of spatially covariant gravity, identifying conditions for propagating a single scalar mode and extending the study to mimetic gravity.

Findings

Degeneracy conditions lead to a single scalar degree of freedom.

The theory's scalar and tensor power spectra are calculated.

Mimetic constraint reduces scalar degrees of freedom from two to one.

Abstract

We make a perturbative analysis of spatially covariant gravity only respecting spatial symmetries, of which the Lagrangian includes the dynamic lapse function and the coupling term of spatial curvature and extrinsic curvature. We show that the theory propagates 2 scalar degrees of freedom, as long as the kinetic terms are degenerate, it propagates a single scalar mode at the linear order. Then we calculate the scalar and tensor power spectra. Finally, we study cosmological perturbations in mimetic gravity in the presence of spatially covariant gravity. The original spatially covariant theory propagates 2 scalar degrees of freedom, and it will propagate only one scalar degree of freedom after adding the mimetic constraint.