Mimetic gravity as DHOST theories

TL;DR

This paper demonstrates that mimetic gravity theories can be reformulated as DHOST theories with an extra gauge symmetry, providing a new classification and analyzing linear perturbations including matter effects.

Contribution

It reformulates mimetic gravity as DHOST theories with an additional gauge symmetry and classifies these theories within this framework.

Findings

Mimetic gravity can be viewed as a subset of DHOST theories.

The classification of mimetic theories within the DHOST framework.

Derivation of the quadratic action for linear perturbations including matter.

Abstract

We show that theories of mimetic gravity can be viewed as degenerate higher-order scalar-tensor (DHOST) theories that admit an extra local (gauge) symmetry in addition to the usual diffeomorphism invariance. We reformulate and classify mimetic theories in this perspective. Using the effective theory of dark energy, recently extended to include DHOST theories, we then investigate the linear perturbations about a homogeneous and isotropic background for all mimetic theories. We also include matter, in the form of a $k$-essence scalar field, and we derive the quadratic action for linear perturbations in this case.