Abstract
In this paper we have obtained some new exact solutions of Einstein’s field equations in a spatially homogeneous and anisotropic Bianchi type-V space-time with perfect fluid distribution along with heat-conduction and decaying vacuum energy density Λ by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. We find that the constant value of deceleration parameter is reasonable for the present day universe. The variation law for Hubble’s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein’s field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The cosmological constant Λ is found to be a decreasing function of time and positive which is corroborated by results from recent supernovae Ia observations. Expressions for look-back time-redshift, neoclassical tests (proper distance d(z)), luminosity distance red-shift and event horizon are derived and their significance are described in detail. The physical and geometric properties of spatially homogeneous and anisotropic cosmological models are discussed.
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Roy, S.R., Prasad, A.: Gen. Relativ. Gravit. 26, 939 (1994)
Farnsworth, D.L.: J. Math. Phys. 8, 2315 (1967)
Collins, C.B.: Commun. Math. Phys. 39, 131 (1974)
Maartens, R., Nel, S.D.: Commun. Math. Phys. 59, 273 (1978)
Wainwright, J., Ince, W.C.W., Marshman, B.J.: Gen. Relativ. Gravit. 10, 259 (1979)
Beesham, A.: Astrophys. Space Sci. 125, 99 (1986)
Maharaj, S.D., Beesham, A.: S. Afr. J. Phys. 17, 34 (1988)
Hewitt, C.G., Wainwright, J.: Phys. Rev. D 46, 4242 (1992)
Camci, U., Yavuz, I., Baysal, H., Tahran, I., Yilmaz, I.: Astrophys. Space Sci. 275, 391 (2000)
Meena, B.L., Bali, R.: Pramana - J. Phys. 62, 1007 (2004)
Pradhan, A., Rai, A.: Astrophys. Space Sci. 291, 149 (2004)
Pradhan, A., Yadav, L., Yadav, A.K.: Czechoslov. J. Phys. 54, 487 (2004)
Aydogdu, O., Salti, M.: Czechoslov. J. Phys. 56, 789 (2006)
Christodoulakis, T., Kofinas, G., Zarikas, V.: Phys. Lett. A 275, 182 (2000)
Christodoulakis, T., Kofinas, G., Papadopoulos, G.O.: Phys. Lett. B 514, 149 (2001)
Christodoulakis, T., Grammenos, T., Helias, C., Kevrekidis, P.G., Spanou, A.: J. Math. Phys. 47, 042505 (2006)
Saha, B.: Astrophys. Space Sci. 302, 83 (2006)
Singh, T., Chaubey, R.: Pramana - J. Phys. 67, 415 (2006)
Singh, T., Chaubey, R.: Pramana - J. Phys. 68, 721 (2007)
Deng, Y.: Gen. Relativ. Gravit. 21, 503 (1989)
Mukherjee, G.: J. Astrophys. Astron. 7, 259 (1986)
Novello, M., Reboucas, M.J.: Astrophys. J. 225, 719 (1978)
Ray, D.: J. Math. Phys. 21, 2797 (1980)
Reboucas, M.J., Lima, J.A.S.: J. Math. Phys. 22, 2699 (1981)
Reboucas, M.J.: Nuovo Cimento B 67, 120 (1982)
Bradley, J.M., Sviestins, E.: Gen. Relativ. Gravit. 16, 1119 (1984)
Sviestins, E.: Gen. Relativ. Gravit. 17, 521 (1985)
Benerjee, A., Sanyal, A.K.: Gen. Relativ. Gravit. 20, 103 (1988)
Coley, A.A.: Gen. Relativ. Gravit. 22, 3 (1990)
Coley, A.A., Hoogen, R.J.: J. Math. Phys. 35, 4117 (1994)
Coley, A.A., Dunn, K.: J. Math. Phys. 33, 1772 (1992)
Singh, J.K.: Astrophys. Space Sci. 310, 241 (2007)
Singh, C.P., Zeyauddin, M., Ram, S.: Int. J. Theor. Phys. 47, 3162 (2008)
Weinberg, S.: Rev. Mod. Phys. 61, 1 (1989)
Weinberg, S.: Gravitation and Cosmology. Wiley, New York (1972)
Abers, E.S., Lee, B.W.: Phys. Rep. 9, 1 (1973)
Langacker, P.: Phys. Rep. 72, 185 (1981)
Frieman, J.A., Waga, I.: Phys. Rev. D 57, 4642 (1998)
Carlberg, R., et al.: Astrophys. J. 462, 32 (1996)
Özer, M., Taha, M.O.: Nucl. Phys. B 287, 776 (1987)
Freese, K., Adams, F.C., Frieman, J.A., Mottola, E.: Nucl. Phys. B 287, 1797 (1987)
Freese, K., Adams, F.C., Frieman, J.A., Mottola, E.: Nucl. Phys. B 287, 797 (1987)
Carvalho, J.C., Lima, J.A.S., Waga, I.: Phys. Rev. D 46, 2404 (1992)
Silviera, V., Waga, I.: Phys. Rev. D 50, 4890 (1994)
Ratra, B., Peebles, P.J.E.: Phys. Rev. D 37, 3406 (1988)
Dolgov, A.D.: In: Gibbons, G.W., Hawking, S.W., Siklos, S.T.C. (eds.) The Very Early Universe. Cambridge University Press, Cambridge (1983)
Dolgov, A.D., Sazhin, M.V., Zeldovich, Ya.B.: Basics of Modern Cosmology. Editions Frontiers (1990)
Dolgov, A.D.: Phys. Rev. D 55, 5881 (1997)
Sahni, V., Starobinsky, A.: Int. J. Mod. Phys. D 9, 373 (2000) 373
Zeldovich, Ya.B.: Sov. Phys., Usph. 11, 381 (1968)
Carroll, S.M., Press, W.H., Turner, E.L.: Ann. Rev. Astron. Astrophys. 30, 499 (1992)
Perlmutter, S., et al.: Astrophys. J. 483, 565 (1997)
Perlmutter, S., et al.: Nature 391, 51 (1998)
Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999)
Riess, A.G., et al.: Astron. J. 116, 1009 (1998)
Riess, A.G., et al.: Astrophys. J. 607, 665 (2004)
Vilenkin, A.: Phys. Rep. 121, 265 (1985)
Garnavich, P.M., et al.: Astrophys. J. 493, L53 (1998)
Garnavich, P.M., et al.: Astrophys. J. 509, 74 (1998)
Carmeli, M., Kuzmenko, T.: Int. J. Theor. Phys. 41, 131 (2002)
Behar, S., Carmeli, M.: Int. J. Theor. Phys. 39, 1375 (2002)
Schmidt, B.P., et al.: Astrophys. J. 507, 46 (1998)
Gasperini, M.: Phys. Lett. B 194, 347 (1987)
Gasperini, M.: Class. Quantum Gravity 5, 521 (1988)
Berman, M.S.: Int. J. Theor. Phys. 29, 567 (1990)
Berman, M.S.: Int. J. Theor. Phys. 29, 1419 (1990)
Berman, M.S.: Phys. Rev. D 43, 75 (1991)
Berman, M.S., Som, M.M.: Int. J. Theor. Phys. 29, 1411 (1990)
Berman, M.S., Som, M.M., Gomide, F.M.: Gen. Relativ. Gravit. 21, 287 (1989)
Berman, M.S., Gomide, F.M.: Gen. Relativ. Gravit. 22, 625 (1990)
Peebles, P.J.E., Ratra, B.: Astrophys. J. 325, L17 (1988)
Chen, W., Wu, Y.S.: Phys. Rev. D 41, 695 (1990)
Sattar, A., Vishwakarma, R.G.: Pramana J. Phys. 47, 41 (1996)
Gariel, J., Denmat, G. Le: Class. Quantum Gravity 16, 149 (1999)
Pradhan, A.: Fizika B (Zagreb) 16, 205 (2007)
Pradhan, A.: Commun. Theor. Phys. 51, 367 (2009)
Pradhan, A., Yadav, V.K.: Int. J. Mod. Phys. D 11, 983 (2002)
Pradhan, A., Pandey, H.R.: Int. J. Mod. Phys. D 12, 941 (2003)
Pradhan, A., Srivastava, S.K., Jotania, K.R.: Czechoslov. J. Phys. 54, 255 (2004)
Pradhan, A., Pandey, P.: Czechoslov. J. Phys. 55, 749 (2005)
Pradhan, A., Pandey, P.: Astrophys. Space Sci. 301, 127 (2006)
Pradhan, A., Pandey, P., Singh, S.K.: Int. J. Theor. Phys. 46, 1584 (2007)
Pradhan, A., Jotania, K., Singh, A.: Braz. J. Phys. 38, 167 (2008)
Pradhan, A., Rai, V., Jotania, K.: Commun. Theor. Phys. 50, 279 (2008)
Pradhan, A., Pandey, P., Jotania, K., Yadav, M.K.: Int. J. Theor. Phys. 46, 2774 (2007)
Abdel-Rahaman, A.-M.M.: Gen. Relativ. Gravit. 22, 655 (1990)
Abdel-Rahaman, A.-M.M.: Phys. Rev. D 45, 3492 (1992)
Vishwakarma, R.G.: Class. Quantum Gravity 17, 3833 (2000)
Ellis, G.F.R., MacCallum, M.A.H.: Commun. Math. Phys. 12, 108 (1969)
Ryan, M.P.Jr., Shepley, L.C.: Homogeneous Relativistic Cosmology. Princeton University Press, Princeton (1975)
Bali, R., Singh, D.K.: Astrophys. Space Sci. 300, 387 (2005)
Rao, V.U., Vinutha, T., Shanthi, M.V.: Astrophys. Space Sci. 312, 189 (2007)
Rao, V.U., Vinutha, T., Shanthi, M.V.: Astrophys. Space Sci. 314, 213 (2008)
Rao, V.U., Vinutha, T., Shanthi, M.V., Sireesha, K.V.S.: Astrophys. Space Sci. 315, 211 (2008)
Rao, V.U., Vinutha, T., Shanthi, M.V., Kumari, G.S.D.: Astrophys. Space Sci. 317, 89 (2008)
Tiwari, R.K.: Fizika B 18, 9 (2009)
Singh, J.P., Baghel, P.S.: Int. J. Phys. 48, 449 (2009)
Singh, C.P., Kumar, S.: Pramana - J. Phys. 68, 707 (2007)
Singh, C.P., Kumar, S.: Astrophys. Space Sci. 310, 31 (2007)
Zeyauddin, M., Ram, S.: Fizika B 18, 87 (2009)
Berman, M.S.: Nuovo Cimento B 74, 182 (1983)
Berman, M.S., Gomide, F.M.: Gen. Relativ. Gravit. 20, 191 (1988)
Singh, C.P., Kumar, S.: Int. J. Mod. Phys. D 15, 419 (2006)
Saha, B., Rikhvitsky, V.: Physica D 219, 168 (2006)
Waga, I.: Astrophys. J. 414, 436 (1993)
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Pradhan, A., Jotania, K. Some Exact Bianchi Type-V Perfect Fluid Cosmological Models with Heat Flow and Decaying Vacuum Energy Density Λ: Expressions for Some Observable Quantities. Int J Theor Phys 49, 1719–1738 (2010). https://doi.org/10.1007/s10773-010-0352-z
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DOI: https://doi.org/10.1007/s10773-010-0352-z