The dark-baryonic matter mass relation for observational verification in Verlinde’s emergent gravity

The dark-baryonic matter mass relation for observational verification in Verlinde’s emergent... Recently, a new interesting idea of origin of gravity has been developed by Verlinde. In this scheme of emergent gravity, where horizon entropy, microscopic de Sitter states and relevant contribution to gravity are involved, an entropy displacement resulting from matter behaves as a memory effect and can be exhibited at sub-Hubble scales, namely, the entropy displacement and its “elastic” response would lead to emergent gravity, which gives rise to an extra gravitational force. Then galactic dark matter effects may origin from such extra emergent gravity. We discuss some concepts in Verlinde’s theory of emergent gravity and point out some possible problems or issues, e.g., the gravitational potential caused by Verlinde’s emergent apparent dark matter may no longer be continuous in spatial distribution at ordinary matter boundary (such as a massive sphere surface). In order to avoid the unnatural discontinuity of the extra emergent gravity of Verlinde’s apparent dark matter, we suggest a modified dark-baryonic mass relation (a formula relating Verlinde’s apparent dark matter mass to ordinary baryonic matter mass) within this framework of emergent gravity. The modified mass relation is consistent with Verlinde’s result at relatively small scales (e.g., $$R<3h_{70}^{-1}$$ R < 3 h 70 - 1  Mpc). However, it seems that, compared with Verlinde’s relation, at large scales (e.g., gravitating systems with $$R>3h_{70}^{-1}$$ R > 3 h 70 - 1  Mpc), the modified dark-baryonic mass relation presented here might be in better agreement with the experimental curves of weak lensing analysis in the recent work of Brouwer et al. Galactic rotation curves are compared between Verlinde’s emergent gravity and McGaugh’s recent model of MOND (Modified Newtonian Dynamics established based on recent galaxy observations). It can be found that Verlinde rotational curves deviate far from those of McGaugh MOND model when the MOND effect (or emergent dark matter) dominates. Some applications of the modified dark-baryonic mass relation inspired by Verlinde’s emergent gravity will be addressed for galactic and solar scales. Potential possibilities to test this dark-baryonic mass relation as well as apparent dark matter effects, e.g., planetary perihelion precession at Solar System scale, will be considered. This may enable to place some constraints on the magnitudes of the MOND characteristic acceleration at the small solar scale. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png General Relativity and Gravitation Springer Journals

The dark-baryonic matter mass relation for observational verification in Verlinde’s emergent gravity

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Physics; Theoretical, Mathematical and Computational Physics; Classical and Quantum Gravitation, Relativity Theory; Differential Geometry; Astronomy, Astrophysics and Cosmology; Quantum Physics
ISSN
0001-7701
eISSN
1572-9532
D.O.I.
10.1007/s10714-018-2382-4
Publisher site
See Article on Publisher Site

Abstract

Recently, a new interesting idea of origin of gravity has been developed by Verlinde. In this scheme of emergent gravity, where horizon entropy, microscopic de Sitter states and relevant contribution to gravity are involved, an entropy displacement resulting from matter behaves as a memory effect and can be exhibited at sub-Hubble scales, namely, the entropy displacement and its “elastic” response would lead to emergent gravity, which gives rise to an extra gravitational force. Then galactic dark matter effects may origin from such extra emergent gravity. We discuss some concepts in Verlinde’s theory of emergent gravity and point out some possible problems or issues, e.g., the gravitational potential caused by Verlinde’s emergent apparent dark matter may no longer be continuous in spatial distribution at ordinary matter boundary (such as a massive sphere surface). In order to avoid the unnatural discontinuity of the extra emergent gravity of Verlinde’s apparent dark matter, we suggest a modified dark-baryonic mass relation (a formula relating Verlinde’s apparent dark matter mass to ordinary baryonic matter mass) within this framework of emergent gravity. The modified mass relation is consistent with Verlinde’s result at relatively small scales (e.g., $$R<3h_{70}^{-1}$$ R < 3 h 70 - 1  Mpc). However, it seems that, compared with Verlinde’s relation, at large scales (e.g., gravitating systems with $$R>3h_{70}^{-1}$$ R > 3 h 70 - 1  Mpc), the modified dark-baryonic mass relation presented here might be in better agreement with the experimental curves of weak lensing analysis in the recent work of Brouwer et al. Galactic rotation curves are compared between Verlinde’s emergent gravity and McGaugh’s recent model of MOND (Modified Newtonian Dynamics established based on recent galaxy observations). It can be found that Verlinde rotational curves deviate far from those of McGaugh MOND model when the MOND effect (or emergent dark matter) dominates. Some applications of the modified dark-baryonic mass relation inspired by Verlinde’s emergent gravity will be addressed for galactic and solar scales. Potential possibilities to test this dark-baryonic mass relation as well as apparent dark matter effects, e.g., planetary perihelion precession at Solar System scale, will be considered. This may enable to place some constraints on the magnitudes of the MOND characteristic acceleration at the small solar scale.

Journal

General Relativity and GravitationSpringer Journals

Published: May 31, 2018

References

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