Friction forces in cosmological models

  • Donato Bini
  • Andrea Geralico
  • Daniele Gregoris
  • Sauro Succi
Regular Article - Theoretical Physics


We investigate the dynamics of test particles undergoing friction forces in a Friedmann–Robertson–Walker (FRW) spacetime. The interaction with the background fluid is modeled by introducing a Poynting–Robertson-like friction force in the equations of motion, leading to measurable (at least in principle) deviations of the particle trajectories from geodesic motion. The effect on the peculiar velocities of the particles is investigated for various equations of state of the background fluid and different standard cosmological models. The friction force is found to have major effects on particle motion in closed FRW universes, where it turns the time-asymptotic value (approaching the recollapse) of the peculiar particle velocity from ultra-relativistic (close to light speed) to a co-moving one, i.e., zero peculiar speed. On the other hand, for open or flat universes the effect of the friction is not so significant, because the time-asymptotic peculiar particle speed is largely non-relativistic also in the geodesic case.


Friction Force Peculiar Velocity Closed Universe Geodesic Motion Flat Universe 
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DG is supported by the Erasmus Mundus Joint Doctorate Program by Grant Number 2011-1640 from the EACEA of the European Commission.


  1. 1.
    S. Perlmutter et al., Astrophys. J. 483, 565 (1997) ADSCrossRefGoogle Scholar
  2. 2.
    P.M. Garnavich et al., Astrophys. J. 493, L53 (1998) ADSCrossRefGoogle Scholar
  3. 3.
    P.J.E. Peebles, Principles of Physical Cosmology (Princeton University Press, Princeton, 1993) Google Scholar
  4. 4.
    G.F.R. Ellis, H. van Elst, Cosmological models (Cargèse lectures 1998), in NATO ASIC Proc. 541: Theoretical and Observational Cosmology, ed. by M. Lachièze-Rey (1999), pp. 1–116. arXiv:gr-qc/9812046 CrossRefGoogle Scholar
  5. 5.
    C. Chicone, B. Mashhoon, K. Rosquist, Phys. Rev. D 83, 124029 (2011) ADSCrossRefGoogle Scholar
  6. 6.
    C. Chicone, B. Mashhoon, K. Rosquist, Phys. Lett. A 375, 1427 (2011) ADSMATHCrossRefGoogle Scholar
  7. 7.
    J.H. Poynting, Philos. Trans. R. Soc. 203, 525 (1903) Google Scholar
  8. 8.
    H.P. Robertson, Mon. Not. R. Astron. Soc. 97, 423 (1937) ADSMATHGoogle Scholar
  9. 9.
    D. Bini, A. Geralico, S. Succi, Eur. Phys. J. C 72, 1913 (2012) ADSCrossRefGoogle Scholar
  10. 10.
    D. Bini, D. Gregoris, S. Succi, Europhys. Lett. 97, 40007 (2012) ADSCrossRefGoogle Scholar
  11. 11.
    D. Bini, D. Gregoris, K. Rosquist, S. Succi, Gen. Relativ. Gravit. 44, 2669 (2012) ADSMATHCrossRefGoogle Scholar
  12. 12.
    D. Bini, D. Gregoris, K. Rosquist, S. Succi, Class. Quantum Gravity 30, 025009 (2013) ADSCrossRefGoogle Scholar
  13. 13.
    H. Stephani, D. Kramer, M. MacCallum, C. Hoensealers, E. Herlt, Exact Solutions of Einstein’s Field Equations (Cambridge University Press, Cambridge, 2002) Google Scholar
  14. 14.
    S. Ramaswamy, Annu. Rev. Condens. Matter Phys. 1, 323 (2010) ADSCrossRefGoogle Scholar
  15. 15.
    E.W. Kolb, M.S. Turner, The Early Universe (Addison-Wesley, Reading, 1990) MATHGoogle Scholar
  16. 16.
    A. Kashlinsky, F. Atrio-Barandela, H. Ebeling, A. Edge, D. Kocevski, Astrophys. J. 712, L81 (2010) ADSCrossRefGoogle Scholar
  17. 17.
    D.-C. Dai, W.H. Kinney, D. Stojkovic, J. Cosmol. Astropart. Phys. 04, 015 (2011) ADSCrossRefGoogle Scholar
  18. 18.
    Y.-Z. Ma, C. Gordon, H.A. Feldman, Phys. Rev. D 83, 103002 (2011) ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  • Donato Bini
    • 1
    • 2
    • 3
    • 4
  • Andrea Geralico
    • 2
    • 5
  • Daniele Gregoris
    • 6
    • 7
  • Sauro Succi
    • 1
    • 3
  1. 1.Istituto per le Applicazioni del Calcolo “M. Picone,” CNRRomeItaly
  2. 2.ICRAUniversity of Rome “La Sapienza”RomeItaly
  3. 3.INFN, Sezione di FirenzeSesto Fiorentino (FI)Italy
  4. 4.Astronomical Observatory of TorinoINAFPino Torinese (TO)Italy
  5. 5.Physics DepartmentUniversity of Rome “La Sapienza”RomeItaly
  6. 6.Physics DepartmentUniversity of StockholmStockholmSweden
  7. 7.Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)PotsdamGermany

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