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The European Physical Journal C

, Volume 66, Issue 1–2, pp 295–306 | Cite as

Vacuum fluctuations and topological Casimir effect in Friedmann–Robertson–Walker cosmologies with compact dimensions

  • A. A. SaharianEmail author
  • A. L. Mkhitaryan
Regular Article - Theoretical Physics

Abstract

We investigate the Wightman function, the vacuum expectation values of the field squared and the energy–momentum tensor for a massless scalar field with general curvature coupling parameter in spatially flat Friedmann–Robertson–Walker universes with an arbitrary number of toroidally compactified dimensions. The topological parts in the expectation values are explicitly extracted and in this way the renormalization is reduced to that for the model with trivial topology. In the limit when the comoving lengths of the compact dimensions are very short compared to the Hubble length, the topological parts coincide with those for a conformal coupling and they are related to the corresponding quantities in the flat spacetime by standard conformal transformation. This limit corresponds to the adiabatic approximation. In the opposite limit of large comoving lengths of the compact dimensions, in dependence of the curvature coupling parameter, two regimes are realized with monotonic or oscillatory behavior of the vacuum expectation values. In the monotonic regime and for non-conformally and non-minimally coupled fields the vacuum stresses are isotropic and the equation of state for the topological parts in the energy density and pressures is of barotropic type. For conformal and minimal couplings the leading terms in the corresponding asymptotic expansions vanish and the vacuum stresses, in general, are anisotropic, though the equation of state remains of barotropic type. In the oscillatory regime, the amplitude of the oscillations for the topological part in the expectation value of the field squared can be either decreasing or increasing with time, whereas for the energy–momentum tensor the oscillations are damping. The limits of validity of the adiabatic approximation are discussed.

Keywords

Momentum Tensor Vacuum Energy Density Compact Dimension Wightman Function Cosmological Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    N.D. Birrell, P.C.W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, 1982) zbMATHGoogle Scholar
  2. 2.
    A.A. Grib, S.G. Mamayev, V.M. Mostepanenko, Vacuum Quantum Effects in Strong Fields (Friedmann Laboratory Publishing, St. Petersburg, 1994) Google Scholar
  3. 3.
    A.D. Linde, Particle Physics and Inflationary Cosmology (Harwood Academic, Chur, 1990) Google Scholar
  4. 4.
    A. Linde, J. Cosmol. Astropart. Phys. 0410, 004 (2004) CrossRefMathSciNetADSGoogle Scholar
  5. 5.
    Y.B. Zeldovich, A.A. Starobinsky, Sov. Astron. Lett. 10, 135 (1984) ADSGoogle Scholar
  6. 6.
    Yu.P. Goncharov, A.A. Bytsenko, Phys. Lett. B 160, 385 (1985) CrossRefMathSciNetADSGoogle Scholar
  7. 7.
    Yu.P. Goncharov, A.A. Bytsenko, Phys. Lett. B 169, 171 (1986) CrossRefMathSciNetADSGoogle Scholar
  8. 8.
    Yu.P. Goncharov, A.A. Bytsenko, Class. Quantum Gravity 4, 555 (1987) zbMATHCrossRefMathSciNetADSGoogle Scholar
  9. 9.
    V.M. Mostepanenko, N.N. Trunov, The Casimir Effect and Its Applications (Clarendon, Oxford, 1997) Google Scholar
  10. 10.
    M. Bordag, U. Mohideen, V.M. Mostepanenko, Phys. Rep. 353, 1 (2001) zbMATHCrossRefMathSciNetADSGoogle Scholar
  11. 11.
    E. Elizalde, S.D. Odintsov, A. Romeo, A.A. Bytsenko, S. Zerbini, Zeta Regularization Techniques with Applications (World Scientific, Singapore, 1994) zbMATHGoogle Scholar
  12. 12.
    M. Bordag, G.L. Klimchitskaya, U. Mohideen, V.M. Mostepanenko, Advances in the Casimir Effect (Oxford University Press, Oxford, 2009) CrossRefGoogle Scholar
  13. 13.
    A.A. Bytsenko, G. Cognola, L. Vanzo, S. Zerbini, Phys. Rep. 266, 1 (1996) CrossRefMathSciNetGoogle Scholar
  14. 14.
    M.J. Duff, B.E.W. Nilsson, C.N. Pope, Phys. Rep. 130, 1 (1986) CrossRefMathSciNetADSGoogle Scholar
  15. 15.
    M.J. Duff, B.E.W. Nilsson, C.N. Pope, in Modern Kaluza–Klein Theories, ed. by T. Appelquist, A. Chodos, P.G.O. Freund (Addison Wesley, Menlo Park, 1987) Google Scholar
  16. 16.
    K.A. Milton, Gravit. Cosmol. 9, 66 (2003) zbMATHADSGoogle Scholar
  17. 17.
    E. Elizalde, S. Nojiri, S.D. Odintsov, Phys. Rev D 70, 043539 (2004) CrossRefADSGoogle Scholar
  18. 18.
    E. Elizalde, J. Phys. A 39, 6299 (2006) zbMATHCrossRefMathSciNetADSGoogle Scholar
  19. 19.
    B.R. Greene, J. Levin, J. High Energy Phys. 0711, 096 (2007) CrossRefMathSciNetADSGoogle Scholar
  20. 20.
    P. Burikham, A. Chatrabhuti, P. Patcharamaneepakorn, K. Pimsamarn, J. High Energy Phys. 0807, 013 (2008) CrossRefMathSciNetADSGoogle Scholar
  21. 21.
    A.A. Saharian, M.R. Setare, Phys. Lett. B 659, 367 (2008) CrossRefMathSciNetADSGoogle Scholar
  22. 22.
    S. Bellucci, A.A. Saharian, Phys. Rev. D 77, 124010 (2008) CrossRefMathSciNetADSGoogle Scholar
  23. 23.
    A.A. Saharian, Class. Quantum Gravity 25, 165012 (2008) CrossRefMathSciNetADSGoogle Scholar
  24. 24.
    E.R. Bezerra de Mello, A.A. Saharian, J. High Energy Phys. 0812, 081 (2008) CrossRefMathSciNetADSGoogle Scholar
  25. 25.
    D. Boyanovsky, H.J. de Vega, R. Holman, Phys. Rev. D 49, 2769 (1994) CrossRefADSGoogle Scholar
  26. 26.
    D. Boyanovsky, H.J. de Vega, R. Holman, D.-S. Lee, A. Singh, Phys. Rev. D 51, 4419 (1995) CrossRefADSGoogle Scholar
  27. 27.
    G. Esposito, G. Miele, L. Rosa, P. Santorelli, Class. Quantum Gravity 12, 2995 (1995) zbMATHCrossRefMathSciNetADSGoogle Scholar
  28. 28.
    M. Bordag, J. Lindig, V.M. Mostepanenko, Yu.V. Pavlov, Int. J. Mod. Phys. D 6, 449 (1997) zbMATHCrossRefMathSciNetADSGoogle Scholar
  29. 29.
    M. Bordag, J. Lindig, V.M. Mostepanenko, Class. Quantum Gravity 15, 581 (1998) zbMATHCrossRefMathSciNetADSGoogle Scholar
  30. 30.
    S.A. Ramsey, B.L. Hu, Phys. Rev. D 56, 678 (1997) CrossRefMathSciNetADSGoogle Scholar
  31. 31.
    S.P. Gavrilov, D.M. Gitman, S.D. Odintsov, Int. J. Mod. Phys. A 12, 4837 (1997) zbMATHCrossRefMathSciNetADSGoogle Scholar
  32. 32.
    P.R. Anderson, W. Eaker, Phys. Rev. D 61, 024003 (1999) CrossRefADSGoogle Scholar
  33. 33.
    S. Habib, C. Molina-París, E. Mottola, Phys. Rev. D 61, 024010 (1999) CrossRefADSGoogle Scholar
  34. 34.
    C. Molina-París, P.R. Anderson, S.A. Ramsey, Int. J. Theor. Phys. 40, 2231 (2001) zbMATHCrossRefGoogle Scholar
  35. 35.
    A.A. Grib, Yu.V. Pavlov, in Focus on Quantum Field Theory, ed. by O. Kovras (Nova Science, New York, 2005), pp. 1–21. gr-qc/0505140 Google Scholar
  36. 36.
    E. Elizalde, J. Phys. A 39, 6299 (2006) zbMATHCrossRefMathSciNetADSGoogle Scholar
  37. 37.
    C.A.R. Herdeiro, M. Sampaio, Class. Quantum Gravity 23, 473 (2006) zbMATHCrossRefMathSciNetADSGoogle Scholar
  38. 38.
    L.H. Ford, L. Parker, Phys. Rev. D 16, 245 (1977) CrossRefMathSciNetADSGoogle Scholar
  39. 39.
    T.S. Bunch, P.C.W. Davies, Proc. R. Soc. Lond. A 356, 569 (1977) CrossRefADSGoogle Scholar
  40. 40.
    T.S. Bunch, P.C.W. Davies, J. Phys. A 11, 1315 (1978) CrossRefMathSciNetADSGoogle Scholar
  41. 41.
    S.G. Mamaev, Theor. Math. Phys. 42, 229 (1980) CrossRefGoogle Scholar
  42. 42.
    L.H. Ford, D.J. Toms, Phys. Rev. D 25, 1510 (1982) CrossRefADSGoogle Scholar
  43. 43.
    A. Vilenkin, L.H. Ford, Phys. Rev. D 26, 1231 (1982) CrossRefMathSciNetADSGoogle Scholar
  44. 44.
    C. Pathinayake, L.H. Ford, Phys. Rev. D 37, 2099 (1988) CrossRefADSGoogle Scholar
  45. 45.
    P.C.W. Davies, V. Sahni, Class. Quantum Gravity 5, 1 (1988) CrossRefMathSciNetADSGoogle Scholar
  46. 46.
    V.B. Bezerra, V.M. Mostepanenko, C. Romero, Gravit. Cosmol. 2, 206 (1996) zbMATHADSGoogle Scholar
  47. 47.
    F. Lucchin, S. Matarrese, Phys. Rev. D 32, 1316 (1985) CrossRefADSGoogle Scholar
  48. 48.
    L.F. Abbott, M.B. Wise, Nucl. Phys. B 244, 541 (1987) CrossRefADSGoogle Scholar
  49. 49.
    D. La, P.J. Steinhardt, Phys. Rev. Lett. 62, 376 (1989) CrossRefADSGoogle Scholar
  50. 50.
    D. La, P.J. Steinhardt, Phys. Lett. B 220, 375 (1989) CrossRefADSGoogle Scholar
  51. 51.
    A.B. Burd, J.D. Barrow, Nucl. Phys. B 308, 929 (1988) CrossRefMathSciNetADSGoogle Scholar
  52. 52.
    K.I. Maeda, Phys. Rev. D 37, 858 (1988) CrossRefADSGoogle Scholar
  53. 53.
    S. Kotsakis, P.J. Saich, Class. Quantum Gravity 11, 383 (1994) CrossRefADSGoogle Scholar
  54. 54.
    L.H. Ford, C. Pathinayake, Phys. Rev. D 39, 3642 (1989) CrossRefADSGoogle Scholar
  55. 55.
    E.R. Bezerra de Mello, A.A. Saharian, Phys. Rev. D 78, 045021 (2008) CrossRefADSGoogle Scholar
  56. 56.
    S.G. Mamayev, V.M. Mostepanenko, A.A. Starobinsky, Sov. Phys. JETP 43, 823 (1976) [Zh. Eksp. Teor. Fiz. 70, 1577 (1976)] ADSGoogle Scholar
  57. 57.
    A.A. Saharian, Phys. Rev. D 69, 085005 (2004) CrossRefMathSciNetADSGoogle Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2010

Authors and Affiliations

  1. 1.Department of PhysicsYerevan State UniversityYerevanArmenia
  2. 2.International Centre for Theoretical PhysicsTriesteItaly

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