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 context. 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. We find that all mimetic theories either exhibit a gradient instability, for either the scalar or the tensor modes, or contain an Ostrogradsky-like mode in the scalar sector coupled with matter.
D. Langlois, M. Mancarella, K. Noui, et. al.
Tue, 13 Feb 18
Comments: 21 pages, 1 figure