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

Mimetic gravity as DHOST theories