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Gravitationally non-degenerate Petrov type-I cosmological model filled with viscous fluid in modified Brans-Dicke cosmology. (English) Zbl 1300.83046
Summary: Adding the cosmological term, which is assumed to be variable in Brans-Dicke theory, we have discussed about a cylindrically symmetric cosmological model filled with viscous fluid with free gravitational field of a non-degenerate Petrov type-I. The effect of viscosity on various kinematical parameters has been discussed. Finally, this model has been transformed to the original form [C. Brans and R. H. Dicke, Phys. Rev., II. Ser. 124, 925–935 (1961; Zbl 0103.21402)] of Brans-Dicke theory (including a variable cosmological term).
MSC:
83F05 Cosmology
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
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[1] Petrosian, V, No article title, Int. Astron. Union Symp., 63, 31, (1975)
[2] Zel’dovich, YB, The cosmological constant and the theory of elementary particles, Sov. Phys. Usp., 11, 381-393, (1968)
[3] Linde, AD, Is the Lee constant a cosmological constant, JETP Lett., 19, 183, (1974)
[4] Drietlein, J, Broken symmetry and the cosmological constant, Phys. Rev. Lett., 33, 1243-1244, (1974)
[5] Brans, CH; Dicke, RH, Mach’s principle and a relativistic theory of gravitation, Phys. Rev., 124, 925-935, (1961) · Zbl 0103.21402
[6] Morganstern, RE, Brans-Dicke cosmologies in arbitrary units: solutions in flat Friedmann universes, Phys. Rev. D, 4, 278-282, (1971)
[7] Morganstern, RE, Exact solutions to Brans-Dicke cosmologies in flat Friedmann universes, Phys. Rev. D, 4, 946-954, (1971) · Zbl 1107.83328
[8] Morganstern, RE, Exact solutions to radiation-filled Brans-Dicke cosmologies, Phys. Rev. D, 4, 282-286, (1971)
[9] Morganstern, RE, Cosmological upper limit on the time variation of G, Nature, 232, 109-110, (1971)
[10] Morganstern, RE, Observational constraints imposed by Brans-Dicke cosmologies, Phys. Rev. D, 7, 1570-1579, (1973)
[11] Miyazaki, A, Cosmological solutions for the homogeneous isotropic universe in the Brans-Dicke theory, Prog. Theor. Phys., 60, 321-323, (1978)
[12] Milne, E.A., Mc Crea, W.H.: Newtonian universes and the curvature of space. Quart. J. Math. Oxford Ser. 5, 73-80 · Zbl 0009.04203
[13] Fujii, Y, Scalar-tensor theory of gravitation and spontaneous breakdown of scale invariance, Phys. Rev., D9, 874-876, (1974)
[14] Endo, M; Fukui, T, The cosmological term and a modified Brans-Dicke cosmology gen, Relativ. Gravit., 8, 833-839, (1977)
[15] Dirac, PAM, The cosmological constants, Nature, 139, 323, (1937) · Zbl 0016.18504
[16] Dirac, PAM, Long range forces and broken symmetries, Proc. R. Soc. Lond. A, 333, 403-418, (1973)
[17] Ellis, G.F.R.: In: Sachs, R.K. (ed.) General Relativity and Cosmology, p. 124. Academic, New York and London (1971)
[18] Bergmann, PG, Comments on the scalar-tensor theory, Int. J. Theor. Phys., 1, 25-36, (1968)
[19] Wagoner, RV, Scalar-tensor theory and gravitational waves, Phys. Rev. D, 1, 3209-3216, (1970) · Zbl 06749961
[20] Landau, L.D., Lifschitz, E.M.: Courses of theoretical physics. In: Fluid Mechanics, vol. 6, p. 505. Pergamon Press, Oxford (1963)
[21] Dicke, RH, Mach’s principle and invariance under transformation of units, Phys. Rev., 125, 2163-2167, (1962) · Zbl 0113.45101
[22] Marder, L, Gravitational waves in general relativity. II. the reflexion of cylindrical waves. proc, R. Soc. Lond. A, 246, 133-143, (1958) · Zbl 0080.21801
[23] Roy, SR; Singh, PN, Some viscous fluid cosmological models of plane symmetry, J. Phys. A: Math. Gen., 9, 255-268, (1976)
[24] Ellis, G.F.R.: In: Sachs, R.K. (ed.) General relativity and cosmology, p. 117. Academic, New York and London (1971)
[25] Roy, SR; Prakash, S, A gravitationally non-degerate viscous fluid cosmological model in general relativity, Indian J. Pure Appl. Math., 8, 723-727, (1977)
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