Towards a viable effective field theory of mimetic gravity
  We discuss mimetic gravity theories with direct couplings between the
curvature and higher derivatives of the scalar field, up to the quintic order,
which were proposed to solve the instability problem for linear perturbations
around the FLRW background for this kind of models. Restricting to homogeneous
scalar field configurations in the action, we derive degeneracy conditions to
obtain an effective field theory with three degrees of freedom. However,
performing the Hamiltonian analysis for a generic scalar field we show that
there are in general four or more degrees of freedom. The discrepancy is
resolved because, for a homogeneous scalar field profile,
$\partial_i\varphi\approx 0$, the Dirac matrix becomes singular, resulting in
further constraints, which reduces the number of degrees of freedom to three.
Similarly, in linear perturbation theory the additional scalar degree of
freedom can only be seen by considering a non-homogeneous background profile of
the scalar field. Therefore, restricting to homogeneous scalar fields these
kinds of models provide viable explicitly Lorentz violating effective field
theories of mimetic gravity.
