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Bianchi type-III bulk viscous and barotropic perfect fluid cosmological models in Lyra’s geometry. (English) Zbl 1213.83079

Summary: We have investigated Bianchi type III bulk viscous and barotropic perfect fluid cosmological models in the frame work of Lyra’s geometry. To get deterministic models of universe, we have assumed the three conditions: (i) shear scalar \((\sigma)\) is proportional to the expansion \((\theta)\). This leads to \(B = C^{n}\), where \(B\) and \(C\) are metric potentials. (ii) In presence of viscous fluid, the coefficient of viscosity of dissipative fluid is a power function of mass density \(\xi =\xi_{0} \rho^{m}\), where \(\xi_{0}\) and \(m\) are constant and (iii) in absence of viscosity, a proportionality relation between pressure and energy density of barotropic perfect fluid \(p = \alpha \rho\), where \(\alpha\) is a proportionality constant. In all the cases, we observed that the displacement vector \(\beta\) is large at beginning of the universe and reduces fast during its evolution so that its nature coincide with the behavior of cosmological constant \(\Lambda\).

MSC:

83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83F05 Relativistic cosmology
83C15 Exact solutions to problems in general relativity and gravitational theory
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[1] Weyl, H.: Sitz. Preuss Akad. Wiss., p. 465 (1918)
[2] Lyra, G.: Math. Z. 54, 52 (1951) · Zbl 0042.15902
[3] Sen, D.K.: Z. Phys. 149, 311 (1957)
[4] Sen, D.K., Dunn, K.A.: J. Math. Phys. 12, 578 (1971) · Zbl 0211.24804
[5] Halford, W.D.: Aust. J. Phys. 23, 863 (1970)
[6] Halford, W.D.: J. Math. Phys. 13, 1699 (1972)
[7] Bhamra, K.S.: Aust. J. Phys. 27, 541 (1974)
[8] Karade, T.M., Borikar, S.M.: Gen. Relativ. Gravit. 9, 431 (1978)
[9] Kalyanshetti, S.B., Wagmode, S.M.: Gen. Relativ. Gravit. 14, 823 (1982) · Zbl 0494.53027
[10] Reddy, D.R.K., Innaiah, R.: Astrophys. Space Sci. 123, 49 (1986) · Zbl 0592.76199
[11] Reddy, D.R.K., Wenkateswar, R.: Astrophys. Space Sci. 136, 183 (1987)
[12] Soleng, H.H.: Gen. Relativ. Gravit. 19, 1213 (1987)
[13] Singh, T., Singh, G.P.: J. Math. Phys. 32, 2456 (1991) · Zbl 0736.76084
[14] Singh, T., Singh, G.P.: Nuovo Cim. 106, 617 (1991)
[15] Singh, T., Singh, G.P.: Int. J. Theor. Phys. 31, 1433 (1992)
[16] Rahaman, F.: Int. J. Mod. Phys. D 10, 579 (2001) · Zbl 1155.83318
[17] Pradhan, A.: J. Math. Phys. 50(2), 22501 (2009) · Zbl 1202.83029
[18] Ram, S., Singh, P.: Int. J. Theor. Phys. 31, 2095 (1992)
[19] Bali, R., Chandnani, N.K.: J. Math. Phys. 49, 032502 (2008) · Zbl 1153.85310
[20] Singh, J.P., Tiwari, R.K.: Pramana J. Phys. 70, 565 (2008)
[21] Bali, R., Chandnani, N.K.: Int. J. Theor. Phys. 48, 3101 (2009) · Zbl 1184.83044
[22] Yadav, V.K., Yadav, L., Yadav, A.K.: Rom. J. Phys. 55(7–8), 862 (2010)
[23] Yadav, V.K., Yadav, L., Yadav, A.K.: Fizika B (Zagreb) 19, 29 (2010) · Zbl 1300.41012
[24] Padmanabhan, T., Chitre, S.M.: Phys. Lett. A 120, 433 (1987)
[25] Johri, V.B., Sudharshan, R.: Phys. Lett. A 132, 316 (1988)
[26] Maartens, R.: Class. Quantum Gravity 12, 1455 (1995) · Zbl 0825.83004
[27] Misner, C.W.: Nature 214, 40 (1967)
[28] Misner, C.W.: Astrophys. J. 151, 431 (1968)
[29] Wienberg, S.: Astrophys. J. 168, 175 (1971)
[30] Murphy, J.L.: Phys. Rev. D 8, 4231 (1973)
[31] Nightingale, J.P.: Astrophys. J. 185, 105 (1973)
[32] Heller, M., Klimek, Z.: Astrophys. Space Sci. 33, 37 (1975)
[33] Bali, R., Pradhan, A.: Chin. Phys. Lett. 24, 585 (2007)
[34] Singh, C.P., Kumar, S.: Int. J. Theor. Phys. 48, 925 (2009) · Zbl 1171.83384
[35] Singh, G.P., Kale, A.Y.: Int. J. Theor. Phys. 48, 3158 (2009) · Zbl 1187.83091
[36] Bali, R., Chandnani, N.K.: Int. J. Theor. Phys. 48, 1523 (2009) · Zbl 1171.83342
[37] Yadav, M.K., Pradhan, A., Singh, S.K.: Astrophys. Space Sci. 311, 423 (2007) · Zbl 1132.83320
[38] Bali, R., Tinker, S., Singh, P.: Int. J. Theor. Phys. 49, 1431 (2010) · Zbl 1200.83125
[39] Bali, R., Chandnani, N.K.: Astrophys. Space Sci. 318, 255 (2008)
[40] Thorne, K.S.: Astrophys. J. 148, 51 (1967)
[41] Kantowski, R., Sachs, R.K.: J. Math. Phys. 7, 443 (1966)
[42] Kristian, J., Sachs, R.K.: Astrophys. J. 143, 379 (1966)
[43] Santos, N.O., Dias, R.S., Banerjee, A.: J. Math. Phys. 26, 878 (1985) · Zbl 0562.76124
[44] Zimdahl, W.: Phys. Rev. D 53, 5483 (1996)
[45] Pavon, D., Bafaluy, J., Jou, D.: Class. Quantum Gravity 8, 357 (1991)
[46] Murphy, G.L.: Phys. Rev. D 8, 4231 (1973)
[47] Wienberg, S.: Gravitation and Cosmology. Wiley, New York (1972)
[48] Belinskii, U.A., Kalatnikov, I.M.: Sov. Phys. JETP 42, 205 (1976)
[49] Perlmutter, S., et al.: Astrophys. J. 43, 565 (1997)
[50] Perlmutter, S., et al.: Nature (Landon) 391, 51 (1998)
[51] Riess, A.G.: Astron. J. 116, 1009 (1998)
[52] Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999) · Zbl 1368.85002
[53] Ellis, G.F.R.: General Relativity and Cosmology, p. 117. Academic Press, San Diego (1971) (edited by R.K. Sachs) · Zbl 0337.53058
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