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Mimetic gravity is a modified theory of gravity which is able to incorporatedark matter into the underlying geometry of space-time by isolating theconformal degree of freedom. The theory has been studied extensively in thecosmological regime, as such, we set out to study the implications of thetheory at astrophysical scales. To that end, we carry out the post-Newtonianexpansion of mimetic gravity to lowest post-Newtonian order. We interpret theequations in the Newtonian limit and study some of the implications of thetheory at the solar system scale. Then by establishing some bounds on theasymptotic behavior of the fields we prove that any static sphericallysymmetric space-time with a non trivial mimetic contribution cannot beasymptotically flat. Finally, we study static spherically symmetric solutions.To explain the rotation curves, one needs a logarithmic term in the potential,we show that even though the mimetic fluid can't reconstruct an exactlogarithmic term, it is able to contribute a quasi-logarithmic term whichrecovers the basic qualitative features of galactic rotation curves.

Newtonian and Post-Newtonian Aspects of Mimetic Gravity