Theoretical and Mathematical Physics

, Volume 174, Issue 3, pp 438–445 | Cite as

Exact solutions and particle creation for nonconformal scalar fields in homogeneous isotropic cosmological models

Article

Abstract

We solve the problem of describing scaling factors of a homogeneous isotropic space-time such that the exact solution for the scalar field with a nonconformal coupling to curvature can be obtained from solutions for the conformally coupled field by redefining the mass and momentum. We give explicit expressions in the form of Abelian integrals for the dependence of time on the scaling factor in these cases. We obtain an exact solution for the scalar field coupled to the Gauss-Bonnet-type curvature and show that the corresponding nonconformal contributions can dominate in particle creation by the gravitational field.

Keywords

quantum theory in curved space-time particle creation by gravitational field scalar field exact solution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. A. Grib, S. G. Mamayev, and V.M. Mostepanenko, Vacuum Quantum Effects in Strong Fields [in Russian], Énergoatomizdat, Moscow (1988); English transl., Friedmann Laboratory Publ., St. Petersburg (1994).Google Scholar
  2. 2.
    N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge Monogr. Math. Phys., Vol. 7), Cambridge Univ. Press, Cambridge (1984).MATHGoogle Scholar
  3. 3.
    V. B. Bezerra, V. M. Mostepanenko, and C. Romero, Modern Phys. Lett. A, 12, 145–154 (1997).ADSCrossRefGoogle Scholar
  4. 4.
    M. Bordag, J. Lindig, V. M. Mostepanenko, and Yu. V. Pavlov, Internat. J. Mod. Phys. D, 6, 449–463 (1997).MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    Yu. V. Pavlov, Theor. Math. Phys., 140, 1095–1108 (2004).MATHCrossRefGoogle Scholar
  6. 6.
    C. Lanczos, Ann. Math., 39, 842–850 (1938).MathSciNetCrossRefGoogle Scholar
  7. 7.
    Yu. V. Pavlov, Internat. J. Mod. Phys., 17, 1041–1044 (2002); arXiv:gr-qc/0202041v1 (2002).ADSCrossRefGoogle Scholar
  8. 8.
    Yu. V. Pavlov, Theor. Math. Phys., 126, 92–100 (2001).MATHCrossRefGoogle Scholar
  9. 9.
    Yu. V. Pavlov, “Creation of particles in cosmology: Exact solutions [in Russian],” in: Quantum Theory and Cosmology (V. Yu. Dorofeev and Yu. V. Pavlov, eds.), Friedmann Laboratory Publ., St. Petersburg (2009), pp. 158–171.Google Scholar
  10. 10.
    Yu. V. Pavlov, Uchen. Zap. Kazan. Gos. Un-ta, Ser. Fiz.-Matem. Nauki, 153, No. 3, 65–71 (2011).Google Scholar
  11. 11.
    A. I. Markushevich, Introduction to the Classical Theory of Abelian Functions [in Russian], Nauka, Moscow (1979); English transl. (Transl. Math. Monogr., Vol. 96), Amer. Math. Soc., Providence, R. I. (1992).MATHGoogle Scholar
  12. 12.
    H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 3, Elliptic and Modular Functions: Lame and Mathieu Functions, McGraw-Hill, New York (1955).Google Scholar
  13. 13.
    S. G. Mamaev, V. M. Mostepanenko, and A. A. Starobinskii, Sov. Phys. JETP, 43, 823–830 (1976).ADSGoogle Scholar
  14. 14.
    E. A. Milne, Nature, 130, 9–10 (1932).ADSCrossRefGoogle Scholar
  15. 15.
    S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge Monogr. Math. Phys., Vol. 1), Cambridge Univ. Press, Cambridge (1973).MATHCrossRefGoogle Scholar
  16. 16.
    I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, Acad. Press, New York (1980).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Institute for Problems in Mechanical EngineeringRASSt. PetersburgRussia
  2. 2.Friedmann Laboratory of Theoretical PhysicsSt. PetersburgRussia

Personalised recommendations