Isaac Scientific Publishing

Advances in Astrophysics

Viscous Fluid Bianchi Type V Cosmological Models with Late Time Acceleration

Download PDF (558.1 KB) PP. 224 - 237 Pub. Date: November 1, 2016

DOI: 10.22606/adap.2016.13007

Author(s)

  • J. P. Singh
    Department of Mathematical Sciences, A. P. S. University, Rewa - 486003, India
  • Prashant S. Baghel*
    Department of Mathematical Sciences, A. P. S. University, Rewa - 486003, India
  • Abhay Singh
    Department of Mathematical Sciences, A. P. S. University, Rewa - 486003, India

Abstract

A new class of a spatially homogeneous and anisotropic Bianchi type V cosmological models of the universe for viscous fluid distribution within the framework of general relativity is investigated by applying suitable functional form for the Hubble parameter H which yields models of the universe that describes an early deceleration and late time acceleration. We have found that cosmological term  being very large at initial times relaxes to a genuine cosmological constant at late times. The physical and kinematical parameters of the models are discussed. The models are found to be compatible with the results of recent observations.

Keywords

Bianchi V, viscosity, variable cosmological term, anisotropy.

References

[1] A. G. Riess, L. G. Strolger, J. Tonry, S. Casertano, H. C. Ferguson, B. Mobasher, P. Challis, A. V. Filippenko, S. Jha, W. Li, R. Chornock, R. P. Kirshner, B. Leibundgut, M. Dickinson, M. Livio, M. Giavalisco, C. C. Steidel, T. Bentez, and Z. Tsvetanov, “Type Ia supernova discoveries at z > 1 from the Hubble space telescope: Evidence for past deceleration and constraints on dark energy evolution,” Astrophys. J., vol. 607, pp. 665–687, 2004.

[2] A. G. Riess, A. V. Filippenko, P. Challis, A. Clocchiatti, A. Diercks, P. M. Garnavich, R. L. Gilliland, C. J. Hogan, S. Jha, R. P. Kirshner, B. Leibundgut, M. M. Phillips, D. Reiss, B. P. Schmidt, R. A. Schommer, R. C. Smith, J. Spyromilio, C. Stubbs, N. B. Suntzeff, and J. Tonry, “Observational evidence from supernova for an acelerating universe and a cosmological constant,” Astron. J., vol. 116, pp. 1009–1038, 1998.

[3] S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, P. G. Castro, S. Deustua, S. Fabbro, A. Goobar, D. E. Groom, I. M. Hook, A. G. Kim, M. Y. Kim, J. C. Lee, N. J. Nunes, R. Pain, C. R. Pennypacker, R. Quimby, C. Lidman, R. S. Ellis, M. Irwin, R. G. McMahon, P. Ruiz-Lapuente, N. Walton, B. Schaefer, B. J. Boyle, A. V. Filippenko, T. Matheson, A. S. Fruchter, N. Panagia, H. J. M. Newberg, and W. J. Couch, “Measurements of and  from 42 high-redshift supernovae,” Astrophys. J., vol. 517, pp. 565–586, 1999.

[4] A. R. Liddle, “Acceleration of the universe,” New Astron. Rev., vol. 45, pp. 235–253, 2001.

[5] J. L. Tonry, B. P. Schmidt, B. Barris, P. Candia, P. Challis, A. Clocchiatti, A. L. Coil, A. V. Filippenko, P. Garnavich, C. Hogan, S. T. Holland, S. Jha, R. P. Kirshner, K. Krisciunas, B. Leibundgut, W. Li, T. Matheson, M. M. Phillips, A. G. Riess, R. Schommer, R. C. Smith, J. Sollerman, J. Spyromilio, C. W. Stubbs, and N. B. Suntzeff, “Cosmological results from high-z supernovae,” Astrophys. J., vol. 594, no. 1, pp. 1–24, 2003.

[6] N. Seto, S. Kawamura, and T. Nakamura, “Possibility of direct measurement of the acceleration of the universe using 0.1 Hz band laser interferometer gravitational wave antenna in space,” Phys. Rev. Lett., vol. 87, no. 22, p. 221103, 2001.

[7] A. T. Lee, P. Ade, A. Balbi, J. Bock, J. Borrill, A. Boscaleri, P. de Bernardis, P. G. Ferreira, S. Hanany, V. V. Hristov, A. H. Jaffe, P. D. Mauskopf, C. B. Netterfield, E. Pascale, B. Rabii, P. L. Richards, G. F. Smoot, R. Stompor, C. D. Winant, and J. H. P. Wu, “A high spatial resolution analysis of the MAXIMA ? 1 cosmic microwave background anisotropy data,” Astrophys. J. Lett., vol. 561, no. 1, pp. L1–L6, 2001.

[8] R. Stompor, M. Abroe, P. Ade, A. Balbi, D. Barbosa, J. Bock, J. Borrill, A. Boscaleri, P. de Bernardis, P. G. Ferreira, S. Hanany, V. Hristov, A. H. Jaffe, A. T. Lee, E. Pascale, B. Rabii, P. L. Richards, G. F. Smoot, C. D. Winant, and J. H. P. Wu, “Cosmological implications of the MAXIMA ? 1 high-resolution cosmic microwave background anisotropy measurement,” Astrophys. J. Lett., vol. 561, no. 1, pp. L7–L10, 2001.

[9] D. N. Spergel, L. Verde, H. V. Peiris, E. E. Komatsu, M. R. Nolta, C. L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, L. Page, G. S. Tucker, J. L.Weiland, E.Wollack, and E. L.Wright, “First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Determination of cosmological parameters,” Astrophys. J. Suppl., vol. 148, pp. 175–194, 2003.

[10] J. L. Sievers, J. R. Bond, J. K. Cartwright, C. R. Contaldi, B. S. Mason, S. T. Myers, S. Padin, T. J. Pearson, U.-L. Pen, D. Pogosyan, S. Prunet, A. C. S. Readhead, M. C. Shepherd, P. S. Udomprasert, L. Bronfman, W. L. Holzapfel, and J. May, “Cosmological parameters from cosmic background imager observations and comparisons with BOOMERANG, DASI, and MAXIMA,” Astrophys. J., vol. 591, no. 2, pp. 599–622, 2003.

[11] T. Padmanabhan, “Cosmological constant–the weight of the vacuum,” Phys. Rep., vol. 380, no. 5, pp. 235–320, 2003.

[12] P. J. E. Peebles, “The cosmological constant and dark energy,” Rev. Mod. Phys., vol. 75, pp. 559–606, 2003.

[13] S. M. Carroll, “The cosmological constant,” Living Rev. Relativity, vol. 4, p. 1, 2001.

[14] V. Sahni and A. Starobinsky, “The case for a positive cosmological -term.” Int. J. Mod. Phys. D, vol. 9, pp. 373–444, 2000.

[15] S. Weinberg, “The cosmological constant problem,” Rev. Mod. Phys., vol. 61, pp. 1–24, 1989.

[16] O. Bertolami, “Time dependent cosmological term,” Nuovo Cim. B, vol. 93, pp. 36–42, 1986.

[17] M. ?zer and M. O. Taha, “A possible solution to the main cosmological problems,” Phys. Lett. B, vol. 171, no. 4, pp. 363–365, 1986.

[18] ——, “A model of the universe free of cosmological problems,” Nucl. Phys. B, vol. 287, pp. 776–796, 1987.

[19] K. Freese, F. C. Adams, J. A. Frieman, and E. Mottola, “Cosmology with decaying vacuum energy,” Nucl. Phys. B, vol. 287, pp. 797–814.

[20] J. P. Singh and R. K. Tiwari, “An LRS Bianchi type-I cosmological model with time-dependent  term,” Int. J. Mod. Phys. D, vol. 16, no. 4, pp. 745–755, 2007.

[21] S. Weinberg, “Entropy generation and the survival of protogalaxies in an expanding universe,” Astophys. J., vol. 168, pp. 175–194, 1971.

[22] C. W. Misner, “Transport processes in the primordial fireball,” Nature, vol. 214, pp. 40–41, 1967.

[23] ——, “The isotropy of the universe,” Astrophys. J., vol. 151, pp. 431–457, 1968.

[24] J. D. Nightingale, “Independent investigations concerning bulk viscosity in relativistic homogeneous isotropic cosmologies,” Astrophys. J., vol. 185, pp. 105–114, 1973.

[25] M. Heller and Z. Klimek, “Viscous universes without initial singularity,” Astrophys. Space Sci., vol. 33, no. 2, pp. 37–39, 1975.

[26] S. R. Roy and S. Prakash, “Some solutions of Einstein-Maxwell equations for cylindrically symmetric spacetime with two degrees of freedom in general relativity,” Ind. J. Pure Appl. Math., vol. 8, no. 9, pp. 1132–1142, 1977.

[27] R. Bali and D. R. Jain, “A gravitationally non-degenerate cosmological model with expanding and shearing viscous fluid in general relativity,” Astrophys. Space Sci., vol. 139, no. 1, pp. 175–181, 1987.

[28] ——, “Some expanding and shearing viscous fluid cosmological models in general relativity,” Astrophys. Space Sci., vol. 141, no. 2, pp. 207–216, 1988.

[29] Ø. Grøn, “Viscous inflationary universe models,” Astrophys. Space Sci., vol. 173, no. 2, pp. 191–225, 1990.

[30] A. Pradhan, “Cylindrically symmetric viscous fluid universe in Lyra geometry,” J. Math. Phys., vol. 50, no. 2, pp. 022 501–022 501, 2009.

[31] ——, “Plane symmetric viscous fluid universe with decaying vacuum energy density ,” FIZIKA B, vol. 18, no. 2, pp. 61–80, 2009.

[32] B. Saha, “Bianchi type I universe with viscous fluid,” Mod. Phys. Lett. A, vol. 20, pp. 2127–2143, 2005.

[33] B. Saha and V. Rikhvitsky, “Anisotropic cosmological models with spinor field and viscous fluid in the presence of a  term: qualitative solutions,” J. Phys. A, vol. 40, no. 46, pp. 14 011–14 028, 2007.

[34] C. P. Singh, S. Kumar, and A. Pradhan, “Early viscous universe with variable gravitational and cosmological ‘constants’,” Class. Quantum Grav., vol. 24, no. 2, pp. 455–474, 2007.

[35] J. P. Singh, “Bulk viscous Bianchi type V cosmological models with decaying cosmological term ,” Int. J. Theor. Phys., vol. 49, no. 11, pp. 2734–2744, 2010.

[36] R. Bali and P. Kumawat, “Bulk viscous L.R.S. Bianchi type V tilted stiff fluid cosmological model in general relativity,” Phys. Lett. B, vol. 665, no. 5, pp. 332–337, 2008.

[37] J. P. Singh, “A cosmological model with both deceleration and acceleration,” Astrophys. Space Sci., vol. 318, no. 1, pp. 103–107, 2008.

[38] A. Pradhan, R. Jaiswal, K. Jotania, and R. K. Khare, “Dark energy models with anisotropic fluid in Bianchi type-VI0 space-time with time dependent deceleration parameter,” Astrophys. Space Sci., vol. 337, no. 1, pp. 401–413, 2012.

[39] M. S. Berman, “A special law of variation for Hubble’s parameter,” Nuovo Cimento B, vol. 74, no. 11, pp. 182–186, 1983.

[40] A. Pradhan, A. Rai, and S. Otarod, “A new class of Bianchi type I viscous fluid universe with a time dependent cosmological term,” FIZIKA B, vol. 17, no. 3, pp. 393–404, 2008.

[41] B. Saha, “Bianchi type I universe with viscous fluid,” Mod. Phys. Lett. A, vol. 20, no. 28, pp. 2127–2143, 2005.

[42] N. Mostafapoor and Ø. Grøn, “Viscous CDM universe models,” Astrophys. Space Sci., vol. 333, no. 2, pp. 357–368, 2011.

[43] R. Maartens, “Dissipative cosmology,” Class. Quantum Grav., vol. 12, no. 6, pp. 1455–1466, 1995.