Many Faces of Mimetic Gravity

TL;DR

This paper explores mimetic gravity, a Weyl-symmetric extension of General Relativity, analyzing its theoretical structure, connections to other scalar-tensor theories, and exact solutions in specific spacetime conditions.

Contribution

It provides a detailed analysis of mimetic gravity's theoretical framework, including its relation to Horndeski and Brans-Dicke theories, and derives exact solutions in certain spacetime scenarios.

Findings

Mimetic gravity extends beyond Horndeski theories with a single scalar degree of freedom.

Connections established between mimetic gravity and singular Brans-Dicke theory.

Exact solutions found in shear-free spacetimes without matter.

Abstract

We consider the recently introduced mimetic gravity, which is a Weyl-symmetric extension of the General Relativity and which can play a role of an imperfect fluid-like Dark Matter with a small sound speed. In this paper we discuss in details how this higher- derivative scalar-tensor theory goes beyond the construction by Horndeski, keeping only one scalar degree of freedom on top of two standard graviton polarizations. In particular, we consider representations of the theory in different sets of Weyl-invariant variables and connect this framework to the singular Brans-Dicke theory. Further, we find solution of equations of motion for the mimetic gravity in the synchronous reference frame in a general curved spacetime. This solution is exact in the test-field approximation or in the case of a shear-free spacetime without any other matter.