Embedding theory as new geometrical mimetic gravity

TL;DR

This paper reformulates the embedding theory of gravity as a mimetic gravity model with an additional matter component, using a novel action involving conserved currents and matrix roots, linking it to bimetric theories.

Contribution

It introduces a new action formulation for embedding gravity as mimetic gravity, connecting geometric and matter aspects with conserved currents and matrix root structures.

Findings

The proposed action is equivalent to the original embedding theory.

It generalizes perfect fluid actions for describing additional matter.

Links between embedding theory, mimetic gravity, and bimetric theories are established.

Abstract

It is known that recently proposed model of mimetic gravity can be presented as general relativity with an additional mimetic matter. We discuss a possibility to analogously reformulate the embedding theory, which is the geometrical description of gravity proposed by Regge and Teitelboim, treating it also as general relativity with some additional matter. We propose a form of action which allows to describe this matter in terms of conserved currents. This action turns out to be a generalization of the perfect fluid action, which can be useful in the analysis of the properties of the additional matter. On the other side, the action contains a trace of the root of the matrix product, which is similar to the constructions appearing in bimetric theories of gravity. The action is completely equivalent to the original embedding theory, so it is not just some artificial model, but has a clear geometric sense. We discuss the possible equivalent forms of the theory and ways of study of the appearing equations of motion.