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Observational tests of nonlocal gravity: Galaxy rotation curves and clusters of galaxies

S. Rahvar*

B. Mashhoon†

  • Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada and Department of Physics, Sharif University of Technology, P.O. Box 11155-9161 Tehran, Iran

  • Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA

  • *rahvar@sharif.edu
  • †mashhoonb@missouri.edu
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Phys. Rev. D 89, 104011 – Published 7 May, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.104011

Abstract

A classical nonlocal generalization of Einstein’s theory of gravitation has recently been developed via the introduction of a scalar causal “constitutive” kernel that must ultimately be determined from observational data. It turns out that the nonlocal aspect of gravity in this theory can simulate dark matter; indeed, in the Newtonian regime of nonlocal gravity, we recover the phenomenological Tohline-Kuhn approach to modified gravity. A simple generalization of the Kuhn kernel in the context of nonlocal general relativity leads to a two-parameter modified Newtonian force law that involves an additional repulsive Yukawa-type interaction. We determine the parameters of our nonlocal kernel by comparing the predictions of the theory with observational data regarding the rotation curves of spiral galaxies. The best-fitting stellar mass-to-light ratio turns out to be in agreement with astrophysical models; moreover, our results are consistent with the Tully-Fisher relation for spiral galaxies. Light deflection in nonlocal gravity is consistent with general relativity at solar-system scales, while beyond galactic scales, an enhanced deflection angle is predicted that is compatible with lensing by the effective “dark matter.” Furthermore, we extend our results to the internal dynamics of rich clusters of galaxies and show that the dynamical mass of the cluster obtained from nonlocal gravity is consistent with the measured baryonic mass.

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References (53)

  1. A. Einstein, The Meaning of Relativity (Princeton University Press, Princeton, NJ, 1955).
  2. B. Mashhoon, Phys. Rev. A 47, 4498 (1993).
  3. N. Bohr and L. Rosenfeld, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 12, 8 (1933) [translated in Quantum Theory and Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton University Press, Princeton, NJ, 1983)].
  4. N. Bohr and L. Rosenfeld, Phys. Rev. 78, 794 (1950).
  5. B. Mashhoon, Ann. Phys. (Berlin) 17, 705 (2008).
  6. F. W. Hehl and B. Mashhoon, Phys. Lett. B 673, 279 (2009).
  7. F. W. Hehl and B. Mashhoon, Phys. Rev. D 79, 064028 (2009).
  8. H.-J. Blome, C. Chicone, F. W. Hehl, and B. Mashhoon, Phys. Rev. D 81, 065020 (2010).
  9. B. Mashhoon, in Cosmology and Gravitation, edited by M. Novello and S. E. Perez Begliaffa (Cambridge Scientific Publishers, Cambridge, England, 2011), pp. 1–9.
  10. C. Chicone and B. Mashhoon, J. Math. Phys. (N.Y.) 53, 042501 (2012).
  11. C. Chicone and B. Mashhoon, Phys. Rev. D 87, 064015 (2013).
  12. B. Mashhoon, Classical Quantum Gravity 30, 155008 (2013).
  13. Gauge Theories of Gravitation, edited by M. Blagojević and F. W. Hehl (Imperial College Press, London, 2013).
  14. R. Aldrovandi and J. G. Pereira, Teleparallel Gravity: An Introduction (Springer, New York, 2013).
  15. J. W. Maluf, Ann. Phys. (Berlin) 525, 339 (2013).
  16. J. L. Synge, Relativity: The General Theory (North-Holland, Amsterdam, 1971).
  17. F. G. Tricomi, Integral Equations (Interscience, New York, 1957).
  18. V. C. Rubin and W. K. Ford, Astrophys. J. 159, 379 (1970).
  19. M. S. Roberts and R. N. Whitehurst, Astrophys. J. 201, 327 (1975).
  20. Y. Sofue and V. Rubin, Annu. Rev. Astron. Astrophys. 39, 137 (2001).
  21. J. D. Bekenstein, in Second Canadian Conference on General Relativity and Relativistic Astrophysics, edited by A. Coley, C. Dyer, and T. Tupper (World Scientific, Singapore, 1988), p. 68.
  22. J. E. Tohline, in IAU Symposium 100, Internal Kinematics and Dynamics of Galaxies edited by E. Athanassoula (Reidel, Dordrecht, 1983), p. 205.
  23. J. R. Kuhn and L. Kruglyak, Astrophys. J. 313, 1 (1987).
  24. R. B. Tully and J. R. Fisher, Astron. Astrophys. 54, 661 (1977).
  25. J. W. Moffat and S. Rahvar, Mon. Not. R. Astron. Soc. 436, 1439 (2013); J. W. Moffat, J. Cosmol. Astropart. Phys. 03 (2006) 004.
  26. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964).
  27. D. Clowe, M. Bradač, A. H. Gonzalez, M. Markevitch, S. W. Randall, C. Jones, and D. Zaritsky, Astrophys. J. Lett. 648, L109 (2006).
  28. D. Clowe, S. W. Randall, and M. Markevitch, Nucl. Phys. B, Proc. Suppl. 173, 28 (2007).
  29. K. Fathi, M. Allen, T. Boch, E. Hatziminaoglou, and R. F. Peletier, Mon. Not. R. Astron. Soc. 406, 1595 (2010).
  30. W. J. G. de Blok, F. Walter, E. Brinks, C. Trachternach, S.-H. Oh, and R. C. Kennicutt, Jr., Astron. J. 136, 2648 (2008); F. Walter, E. Brinks, W. J. G. de Blok, F. Bigiel, R. C. Kennicutt, Jr., M. D. Thornley, and A. Leroy, 136, 2563 (2008); A. K. Leroy, F. Walter, E. Brinks, F. Bigiel, W. J. G. de Blok, B. Madore, and M. D. Thornley, 136, 2782 (2008).
  31. W. J. G. de Blok, F. Walter, E. Brinks, C. Trachternach, S.-H. Oh, and R. C. Kennicutt, Jr., Astron. J. 136, 2648 (2008).
  32. R. C. Kennicutt, Jr. et al., Publ. Astron. Soc. Pac. 115, 928 (2003).
  33. C. Flynn, J. Holmberg, L. Portinari, B. Fuchs, and H. Jahreiß, Mon. Not. R. Astron. Soc. 372, 1149 (2006).
  34. M. A. W. Verheijen and R. Sancisi, Astron. Astrophys. 370, 765 (2001).
  35. M. A. W. Verheijen and R. Sancisi, VizieR Online Data Catalog 33700765 (2001).
  36. R. B. Tully, M. A. W. Verheijen, M. J. Pierce, J.-S. Huang, and R. J. Wainscoat, Astron. J. 112, 2471 (1996).
  37. R. H. Sanders and M. A. W. Verheijen, Astrophys. J. 503, 97 (1998).
  38. E. F. Bell and R. S. de Jong, Astrophys. J. 550, 212 (2001).
  39. E. F. Bell, D. H. McIntosh, N. Katz, and M. D. Weinberg, Astrophys. J. Suppl. Ser. 149, 289 (2003).
  40. E. E. Salpeter, Astrophys. J. 121, 161 (1955).
  41. S.-H. Oh, W. J. G. de Blok, F. Walter, E. Brinks, and R. C. Kennicutt, Jr., Astron. J. 136, 2761 (2008).
  42. M. A. W. Verheijen, Astrophys. J. 563, 694 (2001).
  43. J. E. Tohline, Ann. N.Y. Acad. Sci. 422, 390 (1984).
  44. I. I. Shapiro, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2, p. 469.
  45. C. M. Will, Living Rev. Relativity 9, 3 (2006).
  46. C. L. Sarazin, X-ray Emission from Clusters of Galaxies (Cambridge University Press, Cambridge, 1988).
  47. A. Vikhlinin, A. Kravtsov, W. Forman, C. Jones, M. Markevitch, S. S. Murray, and L. Van Speybroeck, Astrophys. J. 640, 691 (2006).
  48. A. Cavaliere and R. Fusco-Femiano, Astron. Astrophys. 70, 677 (1978).
  49. A. Vikhlinin, Astrophys. J. 640, 710 (2006).
  50. S. W. Allen, R. W. Schmidt, and A. C. Fabian, Mon. Not. R. Astron. Soc. 328, L37 (2001).
  51. A. Vikhlinin (private communication).
  52. Y.-T. Lin, S. A. Stanford, P. R. M. Eisenhardt, A. Vikhlinin, B. J. Maughan, and A. Kravtsov, Astrophys. J. Lett. 745, L3 (2012).
  53. J. W. Moffat and S. Rahvar, arXiv:1309.5077.

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Phys. Rev. D 89, 104011– Published 7 May, 2014
  • Received 21 January 2014

© 2014 American Physical Society

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