Dark matter as a gravitational effect in the embedding theory approach

Abstract

We discuss the possibility of explaining observations usually related to the existence of dark matter by passing from the general relativity (GR) theory to a modified theory of gravity, the embedding theory proposed by Regge and Teitelboim. In this approach, it is assumed that our space-time is a four-dimensional surface in a ten-dimensional flat ambient space. This clear geometric interpretation of a change of a variable in the GR action leading to a new theory distinguishes this approach from the known alternatives: mimetic gravity and other variants. After the passage to the modified theory of gravity, additional solutions that can be interpreted as GR solutions with additional fictitious matter appear besides the solutions corresponding to GR. Just in that fictitious matter, one can try to see dark matter, with no need to assume the existence of dark matter as a fundamental object; its role is played by the degrees of freedom of modified gravity. In the embedding theory, the number of degrees of freedom of fictitious matter is sufficiently large, and hence an explanation of all observations without complicating the theory any further can be attempted.

LaTeX, 16 pages, based on a talk given at the VII International Conference "Models of quantum field theory" (MQFT-2022) dedicated to the 82th anniversary of Professor Alexandr Nikolaevich Vasiliev and to the 80th anniversary of Professor Vladimir Dmitrievich Lyakhovski, Saint Petersburg, Russia, 10-14 October 2022

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