Dark matter from non-relativistic embedding gravity

TL;DR

This paper explores how embedding gravity, a modification of General Relativity, can naturally produce a form of non-relativistic matter that mimics dark matter, potentially addressing key issues in cosmology.

Contribution

It demonstrates that solutions of embedding gravity include a non-relativistic matter component that acts as dark matter, with proven stability and explicit equations of motion.

Findings

Embedding matter can serve as cold dark matter.

Solutions are stable and equivalent to GR with additional matter.

Embedding matter exhibits self-interaction potentially solving core-cusp problem.

Abstract

We study the possibility to explain the mystery of the dark matter through the transition from General Relativity to embedding gravity. This modification of gravity, which was proposed by Regge and Teitelboim, is based on a simple string-inspired geometrical principle: our spacetime is considered here as a 4-dimensional surface in a flat bulk. We show that among the solutions of embedding gravity, there is a class of solutions equivalent to solutions of GR with an additional contribution of non-relativistic embedding matter, which can serve as cold dark matter. We prove the stability of such type of solutions and obtain an explicit form of the equations of motion of embedding matter in the non-relativistic limit. According to them, 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.