International Journal of Theoretical Physics

, Volume 51, Issue 12, pp 3951–3962 | Cite as

Particle Creation in Higher Dimensional Space-time with Variable G and Λ

Article
First Online:
Received:
Accepted:

Abstract

In this paper we consider higher dimensional FRW type cosmological models with time-varying gravitational constant G=G(t) and decaying vacuum energy Λ=Λ(t) in context of the open thermodynamical system of particle creation. The particle creation rate is determined by variable G and Λ. An Exact solution of the gravitational field equations is obtained by assuming the exact power-law solution of the scale factor of the universe. We evaluate the various cosmological parameters and discuss their physical significance in detail for radiation and matter-dominated phases of the universe. The solutions are also relevant for quintessence (accelerating) universe. We also discuss the relevance of the solutions for 5-dimensional Kaluza-Klein FRW type model with and without particle creation in radiation and matter-dominated phases as special case. We obtain the solution where the gravitational constant increases with time during no particle creation. The cosmological constant Λ, however, decreases with time in all the cases.

Keywords

Cosmology Exact solutions Particle creation Vacuum energy density 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

The authors express their sincere thanks to the referees for their constructive suggestions to improve the manuscript.

References

  1. 1.
    Bergman, P.G.: Int. J. Theor. Phys. 1, 25 (1968) CrossRefGoogle Scholar
  2. 2.
    Linde, A.O.: JETP Lett. 19, 183 (1974) MathSciNetADSGoogle Scholar
  3. 3.
    Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999) ADSCrossRefGoogle Scholar
  4. 4.
    Riess, A.G., et al.: Astron. J. 116, 1009 (1998) ADSCrossRefGoogle Scholar
  5. 5.
    Overduin, J.M., Cooperstock, F.I.: Phys. Rev. D 58, 043506 (1998) ADSCrossRefGoogle Scholar
  6. 6.
    Berman, M.S., Som, M.M., Gomide, F.M.: Gen. Relativ. Gravit. 21, 287 (1989) MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    Berman, M.S.: Int. J. Theor. Phys. 29, 567 (1990) MATHCrossRefGoogle Scholar
  8. 8.
    Berman, M.S.: Nuovo Cimento B 105, 239 (1990) ADSCrossRefGoogle Scholar
  9. 9.
    Bertolami, O.: Nuovo Cimento B 93, 36 (1986) ADSCrossRefGoogle Scholar
  10. 10.
    Özer, M., Taha, M.O.: Phys. Lett. B 171, 363 (1986) ADSCrossRefGoogle Scholar
  11. 11.
    Özer, M., Taha, M.O.: Nucl. Phys. B 287, 776 (1987) ADSCrossRefGoogle Scholar
  12. 12.
    Weinberg, S.: Rev. Mod. Phys. 61, 1 (1989) MathSciNetADSMATHCrossRefGoogle Scholar
  13. 13.
    Abdel-Rahaman, A.-M.M.: Phys. Rev. D 45, 3497 (1992) ADSCrossRefGoogle Scholar
  14. 14.
    Chen, W., Wu, Y.S.: Phys. Rev. D 42, 4728 (1992) ADSCrossRefGoogle Scholar
  15. 15.
    Freedman, W.L.: Phys. Scr. T 85, 37 (2000) ADSCrossRefGoogle Scholar
  16. 16.
    Dolgov, A.D.: Phys. Rev. D 55, 5881 (1997) ADSCrossRefGoogle Scholar
  17. 17.
    Vishwakarma, R.G.: Gen. Relativ. Gravit. 197, 33 (2001) Google Scholar
  18. 18.
    Vishwakarma, R.G.: Class. Quantum Gravity 19, 4747 (2002) MathSciNetADSMATHCrossRefGoogle Scholar
  19. 19.
    Beesham, A.: Phys. Rev. D 48, 3539 (1999) MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    Peebles, P.J.E., Ratra, B.: Astrophys. J. 325, L17 (1988) ADSCrossRefGoogle Scholar
  21. 21.
    Peebles, P.J.E., Ratra, B.: Phys. Rev. D 37, 3406 (1988) ADSCrossRefGoogle Scholar
  22. 22.
    Sahni, V., Starobinsky, A.: Int. J. Mod. Phys. D 9, 373 (2000) ADSGoogle Scholar
  23. 23.
    Padmanabhan, T.: Phys. Rep. 380, 235 (2003) MathSciNetADSMATHCrossRefGoogle Scholar
  24. 24.
    Dirac, P.A.M.: Nature 139, 323 (1937) ADSMATHCrossRefGoogle Scholar
  25. 25.
    Dirac, P.A.M.: Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 165, 199 (1938) ADSCrossRefGoogle Scholar
  26. 26.
    Brans, C., Dicke, R.H.: Phys. Rev. 124, 925 (1961) MathSciNetADSMATHCrossRefGoogle Scholar
  27. 27.
    Lau, Y.K.: Aust. J. Phys. 38, 547 (1985) ADSGoogle Scholar
  28. 28.
    Lau, Y.K., Prokhovnik, S.J.: Aust. J. Phys. 39, 339 (1986) ADSGoogle Scholar
  29. 29.
    Beesham, A.: Nuovo Cimento B 96, 17 (1986) ADSCrossRefGoogle Scholar
  30. 30.
    Kalligas, D., Wesson, P., Everitt, C.W.F.: Gen. Relativ. Gravit. 24, 351 (1992) MathSciNetADSCrossRefGoogle Scholar
  31. 31.
    Abdel-Rahaman, A.-M.M.: Gen. Relativ. Gravit. 22, 655 (1990) ADSCrossRefGoogle Scholar
  32. 32.
    Abdussattar Vishwakarma, R.G.: Class. Quantum Gravity 14, 945 (1997) ADSMATHCrossRefGoogle Scholar
  33. 33.
    Arbab, A.I.: Gen. Relativ. Gravit. 29, 391 (1998) MathSciNetGoogle Scholar
  34. 34.
    Singh, C.P., Kumar, S., Pradhan, A.: Class. Quantum Gravity 24, 455 (2007) MathSciNetADSMATHCrossRefGoogle Scholar
  35. 35.
    Beesham, A.: Gen. Relativ. Gravit. 26, 159 (1994) MathSciNetADSMATHCrossRefGoogle Scholar
  36. 36.
    Kalligas, D., Wesson, P., Everitt, C.W.F.: Gen. Relativ. Gravit. 27, 645 (1995) MathSciNetADSMATHCrossRefGoogle Scholar
  37. 37.
    Pradhan, A., Chakraborty, I.: Gravit. Cosmol. 7, 55 (2001) MathSciNetMATHGoogle Scholar
  38. 38.
    Saha, B.: Mod. Phys. Lett. A 16, 1287 (2001) MathSciNetADSMATHCrossRefGoogle Scholar
  39. 39.
    Saha, B.: Astrophys. Space Sci. 302, 83 (2006) ADSMATHCrossRefGoogle Scholar
  40. 40.
    Singh, G.P., Kotambar, S., Srivastava, D., Pradhan, A.: Rom. J. Phys. 53, 607 (2008) Google Scholar
  41. 41.
    Weinberg, S., et al.: Physics in Higher Dimensions. World Scientific, Singapore (1986) Google Scholar
  42. 42.
    Kaluza, T.: Sitz. Preuss. Akad. Wiss. Phys.-Math. K 1, 966 (1921) Google Scholar
  43. 43.
    Klein, O.: Z. Phys. 37, 895 (1926) ADSMATHCrossRefGoogle Scholar
  44. 44.
    Witten, E.: Phys. Lett. B 144, 351 (1984) MathSciNetADSCrossRefGoogle Scholar
  45. 45.
    Appelquist, T., Chodos, A., Freund, P.G.O.: Modern Kaluza-Klein Theories. Addison-Wesley, Reading (1987) MATHGoogle Scholar
  46. 46.
    Overduin, J.M., Wesson, P.S.: Phys. Rep. 283, 303 (1997) MathSciNetADSCrossRefGoogle Scholar
  47. 47.
    Chatterjee, S., Bhui, B.: Mon. Not. R. Astron. Soc. 247, 57 (1990) MathSciNetADSMATHGoogle Scholar
  48. 48.
    Banerjee, A., Bhui, B.: Astron. Astrophys. 232, 305 (1990) ADSMATHGoogle Scholar
  49. 49.
    Singh, G.P., Kotambkar, S.: Gen. Relativ. Gravit. 33, 621 (2001) MathSciNetADSMATHCrossRefGoogle Scholar
  50. 50.
    Singh, G.P., Kotambkar, S.: Gravit. Cosmol. 9, 206 (2003) MathSciNetADSMATHGoogle Scholar
  51. 51.
    Singh, G.P., Kotambkar, S., Pradhan, A.: Int. J. Mod. Phys. D 12, 853 (2003) MathSciNetADSCrossRefGoogle Scholar
  52. 52.
    Khadekar, G.S., Kamdi, V., Pradhan, A., Otarod, S.: Astrophys. Space Sci. 310, 141 (2007) ADSCrossRefGoogle Scholar
  53. 53.
    Prigogine, I., Geheniau, J., Gunzig, E., Nardone, P.: Proc. Natl. Acad. Sci. USA 85, 7428 (1988) MathSciNetADSCrossRefGoogle Scholar
  54. 54.
    Prigogine, I., Geheniau, J., Gunzig, E., Nardone, P.: Gen. Relativ. Gravit. 21, 767 (1989) MathSciNetADSMATHCrossRefGoogle Scholar
  55. 55.
    Sudharsan, R., Johri, V.B.: Gen. Relativ. Gravit. 26, 41 (1994) MathSciNetADSCrossRefGoogle Scholar
  56. 56.
    Harko, T., Mak, M.K.: Astrophys. Space Sci. 253, 161 (1997) MathSciNetADSMATHCrossRefGoogle Scholar
  57. 57.
    Harko, T., Mak, M.K.: Gen. Relativ. Gravit. 31, 849 (1999) MathSciNetADSMATHCrossRefGoogle Scholar
  58. 58.
    Harko, T., Mak, M.K.: Class. Quantum Gravity 16, 2741 (1999) MathSciNetADSMATHCrossRefGoogle Scholar
  59. 59.
    Tegmark, M., et al.: Astrophys. J. 606, 70 (2004) CrossRefGoogle Scholar
  60. 60.
    Weinberg, S.: Gravitation and Cosmology. Wiley, New York (1972) Google Scholar
  61. 61.
    Maartens, R.: Class. Quantum Gravity 12, 1455 (1995) MathSciNetADSMATHCrossRefGoogle Scholar
  62. 62.
    Pradhan, A., Jaiswal, R., Jotania, K., Khare, R.K.: Astrophys. Space Sci. 337, 401 (2012) ADSMATHCrossRefGoogle Scholar
  63. 63.
    Vishwakarma, R.G.: Mon. Not. R. Astron. Soc. 345, 545 (2003) ADSCrossRefGoogle Scholar
  64. 64.
    Berman, M.S.: Phys. Rev. D 43, 1075 (1991) ADSCrossRefGoogle Scholar
  65. 65.
    Rebelo, R.: Nucl. Phys. B, Proc. Suppl. 114, 3 (2003) ADSCrossRefGoogle Scholar
  66. 66.
    Koopmans, L.V.E., et al.: Astrophys. J. 599, 70 (2003) ADSCrossRefGoogle Scholar
  67. 67.
    Abdel Rahaman, A.-M.M.: Gen. Relativ. Gravit. 22, 665 (1990) ADSCrossRefGoogle Scholar
  68. 68.
    Weinberg, S.: Gravitation and Cosmology. Wiley, New York (1971) Google Scholar
  69. 69.
    Abdel Rahaman, A.-M.M.: Phys. Rev. D 45, 3497 (1992) ADSCrossRefGoogle Scholar
  70. 70.
    Levit, L.S.: Lett. Nuovo Cimento 29, 23 (1980) ADSCrossRefGoogle Scholar
  71. 71.
    Sistero, R.F.: Gen. Relativ. Gravit. 23, 1265 (1991) MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Applied MathematicsDelhi Technological UniversityDelhiIndia
  2. 2.Department of Mathematical SciencesUniversity of ZululandKwa-DlangezwaSouth Africa

Personalised recommendations