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Computing general-relativistic effects from Newtonian N-body simulations: Frame dragging in the post-Friedmann approach

Marco Bruni*, Daniel B. Thomas†, and David Wands‡

  • Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth PO1 3FX, United Kingdom

  • *marco.bruni@port.ac.uk
  • †daniel.b.thomas@port.ac.uk
  • ‡david.wands@port.ac.uk
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Phys. Rev. D 89, 044010 – Published 19 February, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.044010

Abstract

We present the first calculation of an intrinsically relativistic quantity, the leading-order correction to Newtonian theory, in fully nonlinear cosmological large-scale structure studies. Traditionally, nonlinear structure formation in standard ΛCDM cosmology is studied using N-body simulations, based on Newtonian gravitational dynamics on an expanding background. When one derives the Newtonian regime in a way that is a consistent approximation to the Einstein equations, the first relativistic correction to the usual Newtonian scalar potential is a gravitomagnetic vector potential, giving rise to frame dragging. At leading order, this vector potential does not affect the matter dynamics, thus it can be computed from Newtonian N-body simulations. We explain how we compute the vector potential from simulations in ΛCDM and examine its magnitude relative to the scalar potential, finding that the power spectrum of the vector potential is of the order 10−5 times the scalar power spectrum over the range of nonlinear scales we consider. On these scales the vector potential is up to two orders of magnitudes larger than the value predicted by second-order perturbation theory extrapolated to the same scales. We also discuss some possible observable effects and future developments.

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References (38)

  1. K. Tomita, Prog. Theor. Phys. 85, 1041 (1991).
  2. M. Shibata and H. Asada, Prog. Theor. Phys. 94, 11 (1995).
  3. S. Matarrese and D. Terranova, Mon. Not. R. Astron. Soc. 283, 400 (1996).
  4. M. Takada and T. Futamase, Mon. Not. R. Astron. Soc. 306, 64 (1999).
  5. C. Carbone and S. Matarrese, Phys. Rev. D 71, 043508 (2005).
  6. J.-c. Hwang, H. Noh, and D. Puetzfeld, J. Cosmol. Astropart. Phys. 03 (2008) 010.
  7. N. E. Chisari and M. Zaldarriaga, Phys. Rev. D 83, 123505 (2011).
  8. S. R. Green and R. M. Wald, Phys. Rev. D 85, 063512 (2012).
  9. I. Milillo, D. Bertacca, M. Bruni, and A. Maselli (to be published).
  10. M. Bruni, R. Crittenden, K. Koyama, R. Maartens, C. Pitrou, and D. Wands, Phys. Rev. D 85, 041301 (2012).
  11. M. Bruni, J. C. Hidalgo, N. Meures, and D. Wands, Astrophys. J. (in press).
  12. S. Chandrasekhar, Astrophys. J. 142, 1488 (1965).
  13. J. M. Bardeen, Phys. Rev. D 22, 1882 (1980).
  14. R. Owen et al., Phys. Rev. Lett. 106, 151101 (2011).
  15. C. W. F. Everitt et al., Phys. Rev. Lett. 106, 221101 (2011).
  16. I. Ciufolini and E. C. Pavlis, Nature (London) 431, 958 (2004).

  17. There are computations of gravitational waves produced by halo formation using a triaxial collapse model [18], and by galaxy mergers using N-body simulations on galactic scales using specific initial conditions [19, 20], but our vector potential is directly extracted from the fully nonlinear cosmological density field as computed from N-body simulations on cosmological scales using standard initial conditions. Gravitational waves are subleading with respect to the vector potential, see below.

  18. C. Carbone, C. Baccigalupi, and S. Matarrese, Phys. Rev. D 73, 063503 (2006).
  19. V. Quilis, A. C. González-Garcı́a, D. Saez, and J. A. Font, Phys. Rev. D 75, 104008 (2007).
  20. T. Inagaki, K. Takahashi, S. Masaki, and N. Sugiyama, Phys. Rev. D 82, 124007 (2010).
  21. C.-P. Ma and E. Bertschinger, Astrophys. J. 455, 7 (1995).
  22. S. Matarrese, S. Mollerach, and M. Bruni, Phys. Rev. D 58, 043504 (1998).
  23. K. A. Malik and D. Wands, Phys. Rep. 475, 1 (2009).
  24. I. Milillo, Ph.D. thesis, University of Portsmouth, 2010.
  25. S. Pueblas and R. Scoccimarro, Phys. Rev. D 80, 043504 (2009).
  26. J.-c. Hwang and H. Noh, J. Cosmol. Astropart. Phys. 04 (2013) 035.
  27. V. Springel, Mon. Not. R. Astron. Soc. 364, 1105 (2005).
  28. M. Crocce, S. Pueblas, and R. Scoccimarro, Mon. Not. R. Astron. Soc. 373, 369 (2006).
  29. R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles (McGraw-Hill, New York, 1981).
  30. M. C. Cautun and R. van de Weygaert, arXiv:1105.0370.
  31. W. E. Schaap and R. van de Weygaert, Astron. Astrophys. 363, L29 (2000).
  32. R. van de Weygaert and W. Schaap, in Data Analysis in Cosmology, edited by V. J. Martı́nez, E. Saar, E. Martı́nez-González, and M.-J. Pons-Borderı́a, Lecture Notes in Physics Vol. 665 (Springer Verlag, Berlin, 2009), p. 291.
  33. S. Colombi, A. Jaffe, D. Novikov, and C. Pichon, Mon. Not. R. Astron. Soc. 393, 511 (2009).
  34. D. B. Thomas, M. Bruni, and D. Wands (to be published).
  35. T. H.-C. Lu, K. Ananda, C. Clarkson, and R. Maartens, J. Cosmol. Astropart. Phys. 02 (2009) 023.
  36. S. Mollerach, D. Harari, and S. Matarrese, Phys. Rev. D 69, 063002 (2004).
  37. D. B. Thomas, C. R. Contaldi, and J. Magueijo, Phys. Rev. Lett. 103, 181301 (2009).
  38. S. Dodelson, Modern cosmology (Academic Press, New York, 2003).

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Phys. Rev. D 89, 044010– Published 19 February, 2014
  • Received 18 June 2013

© 2014 American Physical Society

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