Mimetic K-essence

TL;DR

This paper introduces a novel Weyl-invariant scalar-vector-tensor theory combining mimetic dark matter with unimodular gravity, resulting in a model that mimics GR with a k-essence scalar and explores its properties and limitations.

Contribution

It develops a new method to derive mimetic theories from any suitable k-essence and examines the conditions under which they can be realized, also exploring symmetry breaking effects.

Findings

The theory mimics GR with an additional k-essence scalar.

The scale of the k-essence is an integration constant, a global degree of freedom.

The fluid cannot transition through an ultra-relativistic equation of state.

Abstract

We propose a new non-trivial way to combine mimetic dark matter with the mimetic formulation of unimodular gravity. This yields a Weyl-invariant higher-derivative scalar-vector-tensor theory. We demonstrate that on-shell its behavior mimics GR with an additional k-essence scalar. The overall scale of the k-essence arises as an integration constant -- a global degree of freedom. Interestingly, we find that the resulting fluid cannot make transition through ultra-relativistic equation of state. We develop a method to find a mimetic theory corresponding to any eligible k-essence and identify, which k-essences can or cannot be reproduced this way. Finally, we show that abandoning the Weyl symmetry of the setup allows us to obtain both unimodular gravity and mimetic dark matter simultaneously, from one conformal redefinition of the metric.