  We present a detailed investigation of the dynamical behavior of mimetic
gravity with a general potential for the mimetic scalar field. Performing a
phase-space and stability analysis, we show that the scenario at hand can
successfully describe the thermal history of the universe, namely the
successive sequence of radiation, matter, and dark-energy eras. Additionally,
at late times the universe can either approach a de Sitter solution, or a
scaling accelerated attractor where the dark-matter and dark-energy density
parameters are of the same order, thus offering an alleviation of the cosmic
coincidence problem. Applying our general analysis to various specific
potential choices, including the power-law and the exponential ones, we show
that mimetic gravity can be brought into good agreement with the observed
behavior of the universe. Moreover, with an inverse square potential we find
that mimetic gravity offers an appealing unified cosmological scenario where
both dark energy and dark matter are characterized by a single scalar field,
and where the cosmic coincidence problem is alleviated.
