Newtonian and Post-Newtonian Aspects of Mimetic Gravity

Abstract

Mimetic gravity is a modified theory of gravity which is able to incorporate dark matter into the underlying geometry of space-time by isolating the conformal degree of freedom. The theory has been studied extensively in the cosmological regime, as such, in this thesis, we set out to study the implications of the theory at the solar system and galactic scales. To that end, we carry out the post-Newtonian expansion of mimetic gravity to lowest post-Newtonian order. We interpret the equations in the Newtonian limit and study some of the implications of the theory at the astrophysical scale. We solve the associated equations in several special cases. Then by establishing some bounds on the asymptotic behavior of the fields we prove that any static spherically symmetric space-time with a non trivial mimetic contribution cannot be asymptotically 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 exact logarithmic term, it is able to contribute a quasi-logarithmic term which recovers the basic qualitative features of galactic rotation curves.