  Usually when applying the mimetic model to the early universe, higher
derivative terms are needed to promote the mimetic field to be dynamical.
However such models suffer from the ghost and/or the gradient instabilities and
simple extensions cannot cure this pathology. We point out in this paper that
it is possible to overcome this difficulty by considering the direct couplings
of the higher derivatives of the mimetic field to the curvature of the
spacetime.
