Newtonian and Post-Newtonian Aspects of Mimetic Gravity

TL;DR

This paper explores the implications of mimetic gravity at astrophysical scales, analyzing its post-Newtonian behavior, constraints on solutions, and potential to explain galactic rotation curves through quasi-logarithmic contributions.

Contribution

It provides the first post-Newtonian expansion of mimetic gravity and investigates static solutions, showing how mimetic effects influence galactic rotation curves.

Findings

Mimetic gravity cannot produce asymptotically flat static spherically symmetric solutions.

The theory introduces a quasi-logarithmic potential component affecting rotation curves.

Post-Newtonian analysis clarifies the theory's predictions at solar system scales.

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, we set out to study the implications of the theory at astrophysical 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 solar system scale. 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.