NEC violation in mimetic cosmology revisited
  In the context of Einstein gravity, if the null energy condition (NEC) is
satisfied, the energy density in expanding space-times always decreases while
in contracting space-times the energy density grows and the universe eventually
collapses into a singularity. In particular, no non-singular bounce is
possible. It is, though, an open question if this energy condition can be
violated in a controlled way, i.e., without introducing pathologies, such as
unstable negative-energy states or an imaginary speed of sound. In this paper,
we will re-examine the claim that the recently proposed mimetic scenario can
violate the NEC without pathologies. We show that mimetic cosmology is prone to
gradient instabilities even in cases when the NEC is satisfied (except for
trivial examples). Most interestingly, the source of the instability is always
the Einstein-Hilbert term in the action. The matter stress-energy component
does not contribute spatial gradient terms but instead makes the problematic
curvature modes dynamical. We also show that mimetic cosmology can be
understood as a singular limit of known, well-behaved theories involving
higher-derivative kinetic terms and discuss ways of removing the instability.
