Non-relativistic limit of embedding gravity as General Relativity with dark matter

TL;DR

This paper derives a non-relativistic limit of embedding gravity, showing it can mimic cold dark matter with self-interactions, potentially addressing issues like the core-cusp problem in cosmology.

Contribution

It provides the first derivation of the non-relativistic limit of embedding gravity equations, linking it to cold dark matter behavior with self-interactions.

Findings

Embedding matter acts as cold dark matter in the non-relativistic limit.

Embedding matter exhibits self-interactions that may solve the core-cusp problem.

The equations of motion are consistent with a set of first-order dynamical equations.

Abstract

Regge-Teitelboim embedding gravity is the modified gravity based on a simple string-inspired geometrical principle: our spacetime is considered here as a 4-dimensional surface in a flat bulk. This theory is similar to the recently popular theory of mimetic gravity: the modification of gravity appears in both theories as a result of the change of variables in the action of General Relativity. Embedding gravity, as well as mimetic gravity, can be used in explaining the dark matter mystery since, in both cases, the modified theory can be presented as General Relativity with additional fictitious matter (embedding matter or mimetic matter). For the general case, we obtain the equations of motion of embedding matter in terms of embedding function as a set of first-order dynamical equations and constraints consistent with them. Then we construct a non-relativistic limit of these equations, in which the motion of embedding matter turns out to be slow enough so that it can play the role of cold dark matter. The non-relativistic embedding matter turns out to have a certain self-interaction, which could be useful in the context of solving the core-cusp problem that appears in the LambdaCDM model.