×

Cylindrically symmetric inhomogeneous cosmological models with viscous fluid and varying \(\Lambda\). (English) Zbl 1105.83022

Recently solutions for cylindrically symmetric inhomogeneous cosmological models with viscous fluid were obtained [C. Kilinc and I. Yavuz, Astrophys. Space Sci. 249, 131–142 (1997; Zbl 0895.76099)]. Motivated by the situations discussed in the paper above, the authors of the actual paper focus upon the problem of establishing a formalism for studying the general relativistic evolution in the presence of bulk viscosity in an expanding universe. The viscosity coefficient of the bulk viscous fluid is assumed to be a power function of mass density. Without assuming any adhoc law the authors obtain a cosmological constant as a decreasing function of time.

MSC:

83F05 Relativistic cosmology
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)

Citations:

Zbl 0895.76099
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] A. Einstein: inPreuss. Akad. Wiss. Berlin. Sitzber, 1917, p. 142.
[2] W. de Sitter: Proc. Akad. Weteusch, Amsterdam19 (1917) 1217.
[3] E.P. Hubble: Proc. Nat. Acad. Sci. (USA)15 (1929) 168. · JFM 55.0573.05
[4] A. Friedman: Z. Phys.10 (1922) 377.
[5] A. Friedman: Z. Phys.21 (1924) 326.
[6] J. Gunn, B.M. Tinsley: Nature257 (1975) 454.
[7] E.J. Wampler and W.L. Burke: inNew Ideas in Asronomy (Eds. F. Bertola, J.W. Sulentic, and B.F. Madore), Cambridge University Press, Cambridge, 1988, p. 317.
[8] A.D. Sakharov: Doklady Akad. Nauk. SSSR177 (1968) 70; (translation: Soviet Phys. Doklady12 (1968) 1040).
[9] P.J.E. Peebles and B. Ratra: Astrophys. J.325 (1988) L17.
[10] J.V. Narliker, J.-P. Pecker, and J.-P. Vigier: J. Astrophys. Astr.12 (1991) 7.
[11] S. Ray and D. Ray: Astrophys. Space Sci.203 (1993) 211. · Zbl 0781.76101
[12] R.N. Tiwari, S. Ray and S. Bhadra: J. Pure Appl. Math.31 (2000) 1017.
[13] A. Beesham: Phys. Rev. D48 (1993) 3539.
[14] B. Ratra and P.J.E. Peebles: Phys. Rev. D37 (1988) 3406.
[15] A.D. Dolgov: inThe Very Early Universe (Eds. G.W. Gibbons, S.W. Hawking, and S.T.C. Siklos), Cambridge University Press, Cambridge, 1983.
[16] A.D. Dolgov, M.V. Sazhin, and Ya.B. Zeldovich:Basics of Modern Cosmology, Editions Frontiers, 1990.
[17] A.D. Dolgov: Phys. Rev. D55 (1997) 5881.
[18] V. Sahni and A. Starobinsky: Int. J. Mod. Phys. D9 (2000) 373; gr-qc/9904398.
[19] Ya.B. Zeldovich: Sov. Phys. – Uspekhi11 (1968) 381.
[20] O. Bertolami: Nuovo Cimento B93 (1986) 36; Fortschr. Phys.34 (1986) 829.
[21] S. Weinberg: Rev. Mod. Phys.61 (1989) 1. · Zbl 1129.83361
[22] M.S. Berman and M.M. Som: Gen. Rel. Gravit.20 (1988) 191.
[23] M.S. Berman, M.M. Som, and F.M. Gomide: Gen. Rel. Gravit.21 (1989) 287.
[24] S.M. Carroll, W.H. Press, and E.L. Turner: Ann. Rev. Astron. Astrophys.30 (1992) 499.
[25] P.J.E. Peebles: Rev. Mod. Phys.75 (2003) 559; astro-ph/0207347. · Zbl 1205.83082
[26] T. Padmanabhan: Phys. Rep.380 (2003) 235; hep-th/0212290. · Zbl 1027.83544
[27] S. Perlmutteret al.: Astrophys. J.483 (1997) 565, astro-ph/9608192; Nature391 (1998) 51, astro-ph/9712212; Astrophys. J.517 (1999) 565, astro-ph/9608192.
[28] A.G. Riesset al.: Astron. J.116 (1998) 1009; astro-ph/9805201.
[29] A. Vilenkin: Phys. Rep.121 (1985) 265. · Zbl 0966.83541
[30] P.M. Garnavichet al.: Astrophys. J.493 (1998) L53, astro-ph/9710123; Astrophys. J.509 (1998) 74, astro-ph/9806396.
[31] M. Carmeli and T. Kuzmenko: Int. J. Theor. Phys.41 (2002) 131. · Zbl 0992.83060
[32] S. Behar and M. Carmeli: Int. J. Theor. Phys.39 (2002) 1375; astro-ph/000835. · Zbl 0959.83040
[33] B. P. Schmidtet al.: Astrophys. J.507 (1998) 46; astro-ph/9805200.
[34] R.C. Tolman: Proc. Nat. Acad. Sci.20 (1934) 169. · Zbl 0009.04103
[35] H. Bondi: Mon. Not. R. Astro. Soc.107 (1947) 410.
[36] A.H. Taub: Ann. Math.53 (1951) 472; Phys. Rev.103 (1956) 454. · Zbl 0044.22804
[37] N. Tomimura: Nuovo Cimmento B44 (1978) 372.
[38] P. Szekeres: Commun. Math. Phys.41 (1975) 55. · Zbl 0296.53051
[39] C.B. Collins and D.A. Szafron: J. Math. Phys.20 (1979) 2347; J. Math. Phys.20 (1979) 2362.
[40] D.A. Szafron and C.B. Collins: J. Math. Phys.20 (1979) 2354.
[41] J.M.M. Senovilla: Phys. Rev. Lett.64 (1990) 2219. · Zbl 0942.83506
[42] E. Ruiz and J.M.M. Senovilla: Phys. Rev. D45 (1990) 1995.
[43] N. Dadhich, R. Tikekar, and L.K. Patel: Curr. Sci.65 (1993) 694.
[44] L.K. Patel, R. Tikekar, and N. Dadhich: Pramana – J. Phys.49 (1993) 213.
[45] R. Bali and A. Tyagi: Astrophys. Space Sci.173 (1990) 233. · Zbl 0714.76122
[46] A. Pradhan, V.K. Yadav, and N.N. Saste: Int. J. Mod. Phys. D11 (2002) 857. · Zbl 1062.83576
[47] A. Pradhan and H.R. Pandey: Int. J. Mod. Phys. D12 (2003) 941.
[48] A. Pradhan, S.K. Srivastav, and K.R. Jotania: Czech. J. Phys.54 (2004) 255.
[49] C.W. Misner: Nature124 (1967) 40; Astrophys. J.151 (1968) 431.
[50] G. F. R. Ellis: InGeneral Relativity and Cosmology, Enrico Fermi Course, (Ed. R.K. Sachs), Academic, New York, 1979.
[51] B. L. Hu: InAdvance in Astrophysics, (Eds. L.J. Fung and R. Ruffini), World Scientific, Singapore, 1983.
[52] Ø. Grøn: Astrophys. Space Sci.173 (1990) 191. · Zbl 0714.76120
[53] R. Maartens: Class. Quant. Grav.12 (1995) 1455. · Zbl 0825.83004
[54] D. Pavon, J. Bafaluy, and D. Jou: Class. Quant. Grav.8 (1991) 357;
[55] Proc. Hanno Rund Conf. on Relativity and Thermodynamics, (Ed. S.D. Maharaj), University of Natal, Durban, 1996, p. 21.
[56] W. Zimdahl: Phys Rev. D53 (1996) 5483.
[57] N.O. Santos, R.S. Dias, and A. Banerjee: J. Math. Phys.26 (1985) 878. · Zbl 0562.76124
[58] A. Pradhan, V.K. Yadav, and I. Chakrabarty: Int. J. Phys. D10 (2001) 339.
[59] A. Pradhan and V.K. Yadav: Int. J. Phys. D11 (2001) 893. · Zbl 1062.83577
[60] A. Pradhan and I. Aotemshi: Int. J. Phys. D11 (2002) 1419. · Zbl 1062.83575
[61] A. Pradhan, L. Yadav, and A.K. Yadav: Czech. J. Phys.54 (2004) 487.
[62] A. Pradhan and H.R. Pandey: Indian J. Pure Appl. Math.35 (2004) 513.
[63] C.B. Kilinc and I. Yavuz: Astrophys. Space Sci.249 (1997) 131. · Zbl 0895.76099
[64] G.L. Murphy: Phys. Rev. D8 (1973) 4231.
[65] S. Weinberg:Gravitation and Cosmology, Wiley, New York, 1972.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.