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We study the stability of a recently proposed model of scalar-field mattercalled mimetic dark matter or imperfect dark matter. It has been known thatmimetic matter with higher derivative terms suffers from gradient instabilitiesin scalar perturbations. To seek for an instability-free extension of imperfectdark matter, we develop an effective theory of cosmological perturbationssubject to the constraint on the scalar field's kinetic term. This is done byusing the unifying framework of general scalar-tensor theories based on the ADMformalism. We demonstrate that it is indeed possible to construct a model ofimperfect dark matter which is free from ghost and gradient instabilities. As aside remark, we also show that mimetic $F({\cal R})$ theory is plagued with theOstrogradsky instability.

Healthy imperfect dark matter from effective theory of mimetic cosmological perturbations