Bianchi Type- I Viscous Fluid Accelerating Cosmological Models with Time Dependent Q and Λ - Term

Dinkar Singh Chauhan, R.S.Singh, Anirudh Pradhan "Bianchi Type- I Viscous Fluid Accelerating Cosmological Models with Time Dependent Q and Λ - Term", *International Journal of Mathematics Trends and Technology (IJMTT). *V55(3):185-195 March 2018. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

**Abstract**

In present paper, exact solutions of Einstein's field equations are obtained in a spatially homogenous and anisotropic Bianchi type-I space-time in presence of a dissipative fluid with constant and time dependent cosmological term. Einstein's field equations are solved by considering a scale factor a(t)=tet which yields a time dependent deceleration parameter that affords a late time acceleration in the universe. The cosmological constant () is found to be a decreasing function of time and it approaches a small positive value at the present epoch which is corroborated by consequences from recent supernova Ia observations. To get the deterministic solution a barotropic equation of state together with the shear viscosity is proportional to expansion scalar, is also assumed. The physical and geometric properties of cosmological models are also discussed.

**Reference**

[1] L.M. Krauss and M.S. Turner, "The cosmological constant is Back", Gen. Rel. Grav. 27, 1137 (1995).

[2] S. Weinberg, "The cosmological constant problem", Rev. Mod. Phys. D. 61, 1 (1989)

[3] S.L. Adler, "Einstein gravity as a symmetry-breaking effect in quantum field theory", Rev. Mod. Phys. 54, 729 (1982).

[4] S. Weinberg, "A model of Leptons", Phys. Rev. Lett. 19, 1264 (1967).

[5] A.D. Linde, "Is the Lee constant a cosmological constant?", JETP Lett., 19, 183 (1974)

[6] J.M. Overduin and F.I. Cooper stock, "Evolution of the Scale factor with a variable cosmological Term", Phys. Rev. D 58, 043506 (1998).

[7] J.M. Overduin, "Non Singular Models with a variable cosmological Term.", Ap. J. 517, L. 1 (1999).

[8] J.M. Overdin, "Anisotropic Bianchi Type-I Magnetized String Cosmological Models with Decaying Vacuum Energy [1] Density (t).", Phys. Rev. D. 62, 102001 (2000).

[9] H. Liu and P.s. Wesson, "Universe Models with a variable "Cosmological" Constant and a 'big bounce'.", Asrophys. J. 562. 1 (2001).

[10] S. Podariu and B. Ratra, "Supernova Ia constraints on a Time-Variable cosmological 'Constant'.", Asrophys. J. 532, 109 (2000).

[11] K. Croswell, "Cosmological Consequences with Time dependent Λ-term in Bianchi Type-I spa- time.", New Scientist, April 18 (1994).

[12] P.J.E. Peebles and B. Ratra, "Cosmology with a time-variable cosmological 'constant'.", Astrophys. J. 325, L17 (1988).

[13] T. Banks, "Quantum gravity, the cosmological constant and all that", Nucl. Phys. B 249, 332 (1985).

[14] D.N. Spergel, et al., "Wilkinson Microwave Anisotropy Probe (WMPP)", Astrophys. J. Suppl. 170, 377 (2007); astroph/ 0603449.

[15] D.J. Eisenstein, et al. "Deduction of the Baryon Acoustic Peak in the Large- Scale Correlation Function of SDSS Luminous Red Galaxies", Astrophys. J. 633, 560 (2005).

[16] S.M. Carroll, "Why is the universe accelerating?", Conf. C0307282, TTH09, (2003) [AIP conf Proc 743, 16 (2005)].

[17] E.W. Kolb, S. Matarrese and A. Riotto, "On Cosmic Acceleration without dark energy", New J. Phys. 8 322 (2006).

[18] E.W. Kolb, S. Matarrese, A. Notari and A. Riotto, "Phantom field dynamics in loop quantum cosmology", arXiv:hep-th/0503117 (2005)

[19] A. Upadhey, M. Ishak and P.J. Steinhardt, "Dynamical dark energy : current constraints and forecasts", Phys. Rev. D 72, 063501 (2005).

[20] A.G. Riess, et al., "Type Ia Supernova Discoveries at z > 1 from the Hubble space Telescope : Post Deceleration and constraints on Dark energy Evolution", Astrophys. J. 607, 665 (2004).

[21] A.G. Riess, et al., "Narrowing constraints on the early behaviour of dark energy", Astrophys J. 659, 98 (2007).

[22] R.A. Knop., et al., "High Red shift Supernovae observed with HST", Astrophys. J. 598, 102 (2003).

[23] S. Kalita, H.L. Dourah and K. Duorah, Indian J. Phys. 84, 629 (2010).

[24] S. Dey, J.P. Gewali, A.K. Jha, L. Chhaigle and Y.S. Jain, "Quantum dynamics of molecules in 4 He nano-droplets", Indian J. Phys. 85, 1309 (2011).

[25] S. Oli, "Early Viscous Universe with Variable gravitational and cosmological 'constant'.", Indian J. Phys. 85, 755 (2012).

[26] Z. Nourinezhad and S.H. Mehdipour, "Gravitational energy of a non commutative Vaidya Black hole", Indian J. Phys. 86, 919 (2012).

[27] L.D. Landau and E.M. Lifshitz, "Fluid Mechanics, Pergamom", New York (1959) pp. 47.

[28] B. Saha, "Anisotropic cosmological models with a perfect fluid and a term", Astsophye. Space Sci. 302. 83 (2006).

[29] B. Saha and V. Rikhvitsky, "Bianchi Type-I universe with viscous fluid and term", Physica D 219, 169 (2006).

[30] S. Perl mutter, et al., "Discovery of a Supernova explosion at half the age of the universe", Nature 391, 51 (1998)

[31] S. Perl mutter, et al., "Measurement of omega and Lambda from 42 High-Redshift Supernovae", Astrophysical J. 517, 565 (1999).

[32] A.G. Riess, et al., "Observational Evidence from Supernovae for an Accelerating Universe and a cosmological constant", J. 116, 1009 (1998).

[33] S. Kumar and A.K. Yadav, "Some Bianchi Type-V Models of accelerating universe with dark energy", Mod. Phys. Lett. A 26, 647 (2011).

[34] A. Pradhan and H. Amirhashci, "Dark energy model in anisotropic Bianchi type-III space-time with variable EOS parameter", Astrophys. space Sci. 332, 441 (2011).

[35] H. Amirhashchi, A. Pradhan and H. Zainuddin, "An Interacting and Non-interacting Two-fluid dark energy models in FRW universe with time dependent deceleration parameter", Int. J. Theo. Phys. 50, 3529 (2011).

[36] A. Pradhan, A.S. Dubey and R.K. Khare, "Some exact Bianchi type-I Cosmological Models in scalar-tensor theory of gravitation with time dependent deceleration parameter", Rom. J. Phys. 57, 1222 (2012).

[37] L. Amendola "Acceleration at Z > 1 ?", Mon. Not. R. Astron. Soc. 342, 221 (2003).

[38] A.G. Riess, et al., "Support for an accelerating universe and Glimpse of the epoch of deceleration", Astrophys. J. 560, 49 (2001).

[39] A. Pradhan and P. Pandey, "some Bianchi Type-I Viscose fluid Cosmological Models with a variable Cosmological constant", Astrophys. Space Sce. 301, 127 (2006).

[40] C.P. Singh and S. Kumar, "Bianchi Type-I Viscous Fluid Cosmological Models with variable deceleration parameter", Astrophys Space Sci. 323, 407 (2009).

[41] M.A.H. Mac Callum, "A Class of homogeneous cosmological models III : asymptotic behaviour", Common Math. Phys. 18, 2116 (1971).

[42] Y.M. Cho, "Reinterpretation of Jordan Barans- Dicke theory and Kaluza- Klein Cosmology", Phys. Rev. Lett. 68, 3133 (1992).

[43] Ya. B. Zeldovich, "The Equation of State of Ultrahigh Densities and its relativistic Limitations", Soviet Physics-JETP 14, 1143 (1962).

**Keywords**

Bianchi type-I universe, variable deceleration parameters, Dissipative fluid.