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Time Variable Λ and the Accelerating Universe

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Abstract

We perform a deductive study of accelerating Universe and focus on the importance of variable time-dependent Λ in the Einstein’s field equations under the phenomenological assumption, Λ=αH 2 for the full physical range of α. The relevance of variable Λ with regard to various key issues like dark matter, dark energy, geometry of the field, age of the Universe, deceleration parameter and barotropic equation of state has been trivially addressed. The deceleration parameter and the barotropic equation of state parameter obey a straight line relationship for a flat Universe described by Friedmann and Raychaudhuri equations. Both the parameters are found identical for α=1.

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References

  1. Zwicky, F.: Astrophys. J. 86, 217 (1937)

    Article  MATH  ADS  Google Scholar 

  2. Roberts, M.S., Rots, A.H.: Astron. Astrophys. 26, 483 (1973)

    ADS  Google Scholar 

  3. Einasto, J., Kaasik, A., Saar, E.: Nature 250, 309 (1974)

    Article  ADS  Google Scholar 

  4. Tyson, J.A., et al.: Astron. J. 91, 1274 (1986)

    Article  ADS  Google Scholar 

  5. Subramanian, K., Chitre, S.M.: Astrophys. J. 313, 13 (1987)

    Article  ADS  Google Scholar 

  6. Bode, P.W., Bertschinger, E.: Astron. Astrophys. Suppl. 186, 0805 (1995)

    Google Scholar 

  7. Doroshkevich, A.G., Schneider, R.: Astrophys. J. 469, 445 (1996)

    Article  ADS  Google Scholar 

  8. Clowe, D., Randall, S.W., Markevitch, M.: Nucl. Phys. Suppl. 173, 28 (2007)

    Article  ADS  Google Scholar 

  9. Bradac, M., et al.: Astrophys. J. 681, 187 (2008)

    Article  ADS  Google Scholar 

  10. Guth, A.H.: Phys. Rev. D 23, 347 (1981)

    Article  ADS  Google Scholar 

  11. Linde, A.: Phys. Lett. B 108, 389 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  12. Albrecht, A., Steinhardt, P.J.: Phys. Rev. Lett. 48, 1220 (1982)

    Article  ADS  Google Scholar 

  13. Amsler, C., et al.: Phys. Lett. B 667, 1 (2008)

    Article  ADS  Google Scholar 

  14. Sahni, V.: Lect. Notes Phys. 653, 141 (2004)

    ADS  Google Scholar 

  15. Elgarøy, Ø., et al.: Phys. Rev. Lett. 89, 061301 (2002)

    Article  ADS  Google Scholar 

  16. Spergel, D.N., et al.: Astrophys. J. Suppl. 148, 175 (2003)

    Article  ADS  Google Scholar 

  17. Dodelson, S., Widrow, L.M.: Phys. Rev. Lett. 72, 17 (1994)

    Article  ADS  Google Scholar 

  18. Shi, X.-D., Fuller, G.M.: Phys. Rev. Lett. 82, 2832 (1999)

    Article  ADS  Google Scholar 

  19. Dolgov, A.D., Hansen, S.H.: Astropart. Phys. 16, 339 (2002)

    Article  ADS  Google Scholar 

  20. Abazajian, K., Fuller, G.M., Patel, M.: Phys. Rev. D 64, 023501 (2001)

    Article  ADS  Google Scholar 

  21. Abazajian, K., Fuller, G.M., Tucker, W.H.: Astrophys. J. 562, 593 (2001)

    Article  ADS  Google Scholar 

  22. Asaka, T., Blanchet, S., Shaposnikov, M.: Phys. Lett. B 631, 151 (2005)

    Article  ADS  Google Scholar 

  23. Asaka, T., Shaposnikov, M.: Phys. Lett. B 620, 17 (2005)

    Article  ADS  Google Scholar 

  24. Boyarsky, A., Lesgourgues, J., Ruchayskiy, O., Viel, M.: Phys. Rev. Lett. 102, 201304 (2009)

    Article  ADS  Google Scholar 

  25. Gu, P.-H., Hirsch, M., Sarkar, U., Valle, J.W.F.: Phys. Rev. D 79, 033010 (2009)

    Article  ADS  Google Scholar 

  26. Perlmutter, S., et al.: Nature 391, 51 (1998)

    Article  ADS  Google Scholar 

  27. Riess, A.G., et al.: Astron. J. 116, 1009 (1998)

    Article  ADS  Google Scholar 

  28. Guth, A.H., Pi, S.-Y.: Phys. Rev. Lett. 49, 1110 (1982)

    Article  ADS  Google Scholar 

  29. Hawking, S.W.: Phys. Lett. B 115, 295 (1982)

    Article  ADS  Google Scholar 

  30. Bardeen, J.M., Steinhardt, P.J., Turner, M.S.: Phys. Rev. D 28, 679 (1983)

    Article  ADS  Google Scholar 

  31. Tegmark, M., et al.: Astrophys. J. 606, 702 (2004)

    Article  ADS  Google Scholar 

  32. Amendola, L.: Mon. Not. R. Astron. Soc. 342, 221 (2003)

    Article  ADS  Google Scholar 

  33. Riess, A.G.: Astrophys. J. 560, 49 (2001)

    Article  ADS  Google Scholar 

  34. Overduin, J.M., Cooperstock, F.I.: Phys. Rev. D 58, 043506 (1998)

    Article  ADS  Google Scholar 

  35. Sahni, V., Starobinsky, A.: Int. J. Mod. Phys. D 9, 373 (2000)

    ADS  Google Scholar 

  36. Vishwakarma, R.G.: Class. Quantum Gravity 17, 3833 (2000)

    Article  MATH  ADS  Google Scholar 

  37. Astier, P., et al.: Astron. Astrophys. 447, 31 (2006)

    Article  ADS  Google Scholar 

  38. Hsu, S.D.H.: Phys. Lett. B 594, 13 (2004)

    Article  ADS  Google Scholar 

  39. Ray, S., Mukhopadyay, U., Meng, X.-H.: Gravit. Cosmol. 13, 142 (2007)

    MATH  ADS  Google Scholar 

  40. Carmeli, M.: Int. J. Mod. Phys. A 17, 4219 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  41. Zeldovich, Y.B.: JETP Lett. 6, 316 (1967)

    ADS  Google Scholar 

  42. Zeldovich, Y.B.: Sov. Phys. Usp. 11, 381 (1968)

    Article  ADS  Google Scholar 

  43. Guth, A.H.: In: The Inflationary Universe, p. 22. Addison Wesley, New York (1997)

    Google Scholar 

  44. Davies, P.C.W.: Phys. Rev. D 30, 737 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  45. Hogan, C.: Nature 310, 365 (1984)

    Article  ADS  Google Scholar 

  46. Kaiser, N., Stebbins, A.: Nature 310, 391 (1984)

    Article  ADS  Google Scholar 

  47. Blome, J.J., Priester, W.: Naturwissenshaften 71, 528 (1984)

    Article  ADS  Google Scholar 

  48. Weinberg, S.: In: Cosmology, p. 39. Oxford Univ. Press, Oxford (2008)

    Google Scholar 

  49. Milne, E.A.: Relativity, Gravitation and World Structure. Oxford Univ. Press, Oxford (1935)

    Google Scholar 

  50. Kujat, J., et al.: Astrophys. J. 572, 1 (2002)

    Article  ADS  Google Scholar 

  51. Bartelmann, M., et al.: New Astron. Rev. 49, 199 (2005)

    Article  ADS  Google Scholar 

  52. Nojiri, S., Odintsov, S.D.: Phys. Lett. B 649, 440 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  53. Brevik, I., Gorbunova, O.G., Timoshkin, A.V.: Eur. Phys. J. C 51, 179 (2007)

    Article  ADS  Google Scholar 

  54. Usmani, A.A., et al.: Mon. Not. R. Astron. Soc. Lett. 386, L92 (2008)

    Article  ADS  Google Scholar 

  55. Knop, R., et al.: Astrophys. J. 598, 102 (2003)

    Article  ADS  Google Scholar 

  56. Cattoën, C., Visser, M.: Phys. Rev. D 78, 063501 (2008)

    Article  ADS  Google Scholar 

  57. Efstathiou, et al.: DOI: 10.1046/j.1365-87.1999.02433.x

  58. Peebles, P.J.E., Partridge, R.B.: Astrophys. J. 148, 713 (1967)

    Article  ADS  Google Scholar 

  59. Vishwakarma, R.G.: Class. Quantum Gravity 19, 4747 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  60. Cayrel, R., et al.: Nature 409, 691 (2001)

    Article  ADS  Google Scholar 

  61. Ray, S., et al.: Int. J. Theor. Phys. 48, 2499 (2009)

    Article  MATH  Google Scholar 

  62. Mukhopadhyay, U.: Thesis, Ph.D., Jadavpur University, India (2009)

  63. Mukhopadhyay, U., Ray, S.: N. B. U. Math. J. II, 51 (2009)

    Google Scholar 

  64. Mukhopadhyay, U., Ray, S., Rahaman, F.: Int. J. Mod. Phys. D 19, 475 (2010)

    Article  MATH  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Satyabharati Vidyapith, Nabapalli, North 24 Parganas, Kolkata, 700 126, West Bengal, India

    Utpal Mukhopadhyay

  2. Department of Physics, Government College of Engineering & Ceramic Technology, Kolkata, 700 010, West Bengal, India

    Saibal Ray

  3. Department of Physics, Aligarh Muslim University, Aligarh, 202 002, Uttar Pradesh, India

    A. A. Usmani

  4. Department of Physics, A. J. C. Bose Polytechnic, Berachampa, North 24 Parganas, Devalaya, 743 424, West Bengal, India

    Partha Pratim Ghosh

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  1. Utpal Mukhopadhyay
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  2. Saibal Ray
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  3. A. A. Usmani
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  4. Partha Pratim Ghosh
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Correspondence to Saibal Ray.

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Mukhopadhyay, U., Ray, S., Usmani, A.A. et al. Time Variable Λ and the Accelerating Universe. Int J Theor Phys 50, 752–759 (2011). https://doi.org/10.1007/s10773-010-0611-z

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  • DOI: https://doi.org/10.1007/s10773-010-0611-z

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