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Dark matter as a gravitational effect in the embedding theory approach

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Abstract

We discuss a possibility to explain 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. In that theory, 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.

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Notes

  1. \(\Lambda\)-cold dark matter model.

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Acknowledgments

The author is grateful to the organizers of the VII International Conference “Models of quantum field theory” (MQFT-2022) dedicated to the 82th anniversary of Professor Alexandr Nikolaevich Vasil’ev and to the 80th anniversary of Professor Vladimir Dmitrievich Lyakhovski.

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  1. Faculty of Physics, Saint Petersburg State University, St. Petersburg, Russia

    S. A. Paston

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Correspondence to S. A. Paston.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2023, Vol. 216, pp. 559–576 https://doi.org/10.4213/tmf10446.

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Paston, S.A. Dark matter as a gravitational effect in the embedding theory approach. Theor Math Phys 216, 1382–1395 (2023). https://doi.org/10.1134/S004057792309012X

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