Many Faces of Mimetic Gravity
  We consider the recently introduced mimetic gravity, which is a
Weyl-symmetric extension of the General Relativity and which can play a role of
an imperfect fluid-like Dark Matter with a small sound speed. In this paper we
discuss in details how this higher- derivative scalar-tensor theory goes beyond
the construction by Horndeski, keeping only one scalar degree of freedom on top
of two standard graviton polarizations. In particular, we consider
representations of the theory in different sets of Weyl-invariant variables and
connect this framework to the singular Brans-Dicke theory. Further, we find
solution of equations of motion for the mimetic gravity in the synchronous
reference frame in a general curved spacetime. This solution is exact in the
test-field approximation or in the case of a shear-free spacetime without any
other matter.
