2-A Cosmological Model with Varying G and ∧ in General Relativity

Affiliation(s)

Department of Applied Sciences , Sant Baba Bhag Singh Institute of Engineering & Technology, Jalandhar, India.

Goverment Engineering College, Reva, M.P., India.

Department of Applied Sciences , Sant Baba Bhag Singh Institute of Engineering & Technology, Jalandhar, India.

Goverment Engineering College, Reva, M.P., India.

ABSTRACT

Spatially homogeneous and anisotropic Cosmological
models play a significant role in the description of the early stages of evolution
of the universe. The problem of the cosmological constant is still unsettled.
The authors recently considered time dependent G and L with Bianchi type–I Cosmological model .We considered in this paper
homogeneous Bianchi type -I space-time with variable G and L containing matter in the form of a perfect fluid assuming the cosmological
term proportional to R^{-2} (where R is scale factor). Initially the
model has a point type singularity, gravitational constant G (*t*) is decreasing and cosmological
constant L is infinite at this time. When time
increases L decreases. Unlike
in some earlier works we have neither assumed equation of state nor particular
form of G. The model does not approach isotropy, if ‘*t*’ is small .The model is quasi-isotropic for large value of ‘*t*’.

Cite this paper

H. , R. Tiwari and H. Sahota, "2-A Cosmological Model with Varying G and ∧ in General Relativity,"*Open Journal of Applied Sciences*, Vol. 3 No. 1, 2013, pp. 74-78. doi: 10.4236/ojapps.2013.31B1015.

H. , R. Tiwari and H. Sahota, "2-A Cosmological Model with Varying G and ∧ in General Relativity,"

References

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[34] D. Pavon, “Nonequilibrium Fluctions in Cosmic Vacuum Decay,” Physical Review D, Vol. 43, 1991, pp. 375-378. doi：10.1103/PhysRevD.43.375

[35] A. M. M. Abdel-Rahaman, “A Critical Density Cosmological Model with Varying Gravitation and Cosmological Constants,” General Relativity and Gravitation, Vol. 22, No. 6, 1990, pp. 655-663. doi：10.1007/BF00755985

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[37] M. S. Berman and M. M. Som, “Brans-Dicke Models with Time-dependent Cosmological Term,” International Journal of Theory Physics, Vol. 29, 1990, pp. 1411-1414. doi：10.1007/BF00674120

[38] W. Chen and Y. S. Wu, “Implication of a Cosmological Constant Varying as R^{-2} ,” Physical Review D, Vol. 41, 1990, p. 695.

[39] E. A. Milne, “Relativity, Gravitation and World structure,” Oxford University Press, Oxford, 1935.

[40] M. S. Berman, M. M. Som and F. M. Gomide, “Brans-Dicke Static Universes,” General Relativity and Gravitation, Vol. 21, 1989, pp. 287-292. doi：10.1007/BF00764101

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[45] T. L. Chow, “The Variability of the Gravitational Constant,” Nuovo Cimento Lettere, Vol. 31, 1981, pp. 119-120. doi:10.1007/BF02822409

[46] L. S. Levitt, “The Gravitational Constraint at Time Zero,” Nuovo Cimento,Lettere, Serie 2, Vol. 29 , 1980, p. 23.

[1] B. Saha, “Anisotropic Cosmological Models with a Perfect Fluid and a Term,” Astrophysics and Space Science , Vol. 302, No. 1-4, 2006a, pp. 83-91.

[2] B. Saha, “Anisotropic Cosmological Models with a Perfect Fluid and Dark Energy Reexamined,” International Journal of Theoretical Physics, Vol. 45, No. 5, 2006b, pp. 952-964.

[3] B. Saha, “Bianchi Type I Universe With Viscous Fluid,” Modern Physics Letters A, Vol. 20, No. 28, 2005, p. 2127. doi：10.1142/S021773230501830X

[4] B. Saha, “Anisotropic Cosmological Models with Perfect Fluid and Dark Energy,”Chinese, 2005.

[5] R. G. Vishwakarma, “A Model to Explain Varying, G and σ

[6] S. Carneiro and J. A. S. Lima, “Time Dependent Cosmological Term and Holography,” Modern International Journal of Physics A, Vol. 20, No. 11, 2005, p. 2465. doi:10.1142/S0217751X0502478X

[7] J. V. Cunha, R. C. Santos, “The Existence Of An Old Quasar At Z = 3.91 And Its Implications For Λ(T) Deflationary Cosmologies Read,” Modern International Journal of Physics D, Vol. 13, No. 7, 2004, p. 1321. doi.org/10.1142/S0218271804005481

[8] A. G. Riess, et al., Astronomical Journal, pp. 607- 665.

[9] S. W. Allen, et al., “Probing Dark Energy with Constellation-X,” Monthly Notices of the Royal Astronomical Society, Vol. 353, No. 2, 2004, pp. 457-467. doi:10.1111/j.1365-2966.2004.08080.x

[10] J. A. S. Lima “Alternative Dark Energy Models: An Overview,” Brazilian Journal of Physics, Vol. 34, No. 1a, 2004, pp. 194-200. doi：10.1590/S0103-97332004000200009

[11] T. Padmanabhan, “Cosmological Constant the Weight of the Vacuum,” Physics Report, Vol. 380, No. 5-6, 2003, pp. 235-320. doi:10.1016/S0370-1573(03)00120-0

[12] P. J. E. Peebles and B. Ratra, “The Cosmological Constant and Dark Energy,” Reviews of Modern Physics, Vol. 75, No. 2, 2003, pp. 559-606. doi：10.1103/RevModPhys.75.559

[13] R. G. Vishwakarma, “Study of the Magnitude-Redshift Relation for Type Ia Supernovae in a Model Resulting from a Ricci-Symmetry,” General Relativivity and Gravity, Vol. 33, 2001, p. 1973.

[14] R. A. Vishwakarma, “A Study of Angular Size-redshift Relation for Models in Which ∧ Decays as the Energy Density,” Class Quantum Gravity, Vol. 17, 2000, pp. 38-33. doi：10.1088/0264-9381/17/18/317

[15] S. Perlmutter, et al., “Measurements of Ω and Λ from 42 High-Redshift Supernovae,” Astrophysical Journal, 1999, pp. 517- 565.

[16] I. Arbab, “Bianchi Type I Universe with Variable G and Λ,” General Relativity and Gravitation, Vol. 30, No. 9,1998, pp. 1401-1405. doi:0.1023/A:1018856625508

[17] S. Perlmutter, et al., “Discovery of a Supernova Explosion at Half the Age of the Universe,” Nature, Vol. 391, 1998.

[18] A. G. Riess, et al., “Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant,” the Astronphysical Journal, Vol. 116 , 1998, p. 1009.

[19] S. Perlmutter, et al., “Measurements of the Cosmological Parameters Ω and Λ from the First Seven Supernovae at z ≥ 0.35,” the Astrophysical Journal, Vol. 483, No. 2,1997, p. 565.doi：10.1086/304265.

[20] V. Silveira and J. Waga, “Cosmological Properties of a Class of ∧ Decaying Cosmologies,” Physical Review D, Vol. 56, 1997, p. 4625.

[21] J. A. S. Lima and M. Trodden, “Decaying Vacuum Energy and Deflationary Cosmology in Open and Closed Universes,” Physical Review D, Vol. 53, No. 8, 1996, pp. 4280-4286. DOI: 10.1103/PHYSREVD.53.4280）

[22] J. A. S. Lima, “Thermodynamics of Decaying Vacuum Cosmologies,” Physical Review D, Vol. 54, p. 2571.

[23] L. F. B. Torres and I. Waga, “Decaying Lambda Cosmologies and Statistical Properties of Gravitational Lenses,” Monthly Noices of the Royal Astronomical Society, Vol. 279, 1996, pp. 712-726. doi: 10.1093/mnras/279.3.712

[24] D. Kalligas, P. S. Wesson and C. W. F. Everitt, “Bianchi Type I Cosmological Models with VariableG and Λ: A Comment, General Relativity and Gravitivity, Vol. 27, 1995, pp. 645-650. doi：10.1007/BF02108066

[25] A. I. Arbab and A. M. M. Abdel-Rahaman, “Nonsingular Cosmology with a Time-dependent Cosmological Term,” Physical Review D, Vol. 50, 1994, pp. 7725-7728. doi：10.1103/PhysRevD.50.7725

[26] A. Beesham, General Relativity and Gravitivity, Vol. 26 1599.

[27] J. A. S. Lima and J. M. F. Maia, Physical Review D, Vol. 49, 1994, p. 5579.

[28] J. A. S.Lima and J. C. Carvalho, “Dirac's Cosmology with Varying Cosmological Constant,” General Relativity and Gravitivity, Vol. 26, 1994, pp. 909-916. doi10.1007/BF02107147

[29] M. D. Maia and G. S. Silva, “Geometrical Constraints on the Cosmological Constant,” Physical Review D, Vol. 50 , 1994, pp. 7233-7238. doi：10.1103/PhysRevD.50.7233

[30] V. Silveira and J. Waga, “Decaying Λ Cosmologies and Power Spectrum,” Physical Review D, Vol. 50, 1994, pp. 4890-4894. doi：10.1103/PhysRevD.50.4890

[31] J. C. Carvalho, J. A. S. Lima and I. Waga, “Cosmological Consequences of a Time-dependent Term,” Physical Review D, Vol. 46, No. 6, 1992, pp. 2404-2407. doi：10.1103/PhysRevD.46.2404

[32] M. S. Berman, “Cosmological Models with Variable Gravitational and Cosmological Constants,” General Relativity and Gravitation, Vol. 23, 1991a, pp. 465-469. doi：10.1007/BF00756609

[33] M. S. Berman, “Cosmological Models with VariableCosmological Term,” Physical Review D, Vol. 43, 1991b, pp. 1075-1078.

[34] D. Pavon, “Nonequilibrium Fluctions in Cosmic Vacuum Decay,” Physical Review D, Vol. 43, 1991, pp. 375-378. doi：10.1103/PhysRevD.43.375

[35] A. M. M. Abdel-Rahaman, “A Critical Density Cosmological Model with Varying Gravitation and Cosmological Constants,” General Relativity and Gravitation, Vol. 22, No. 6, 1990, pp. 655-663. doi：10.1007/BF00755985

[36] M. Berman, “Static Universe in a Modified Brans- dicke Cosmology,” International Journal of Theoretical Physics, Vol. 29, 1990, pp. 567-570. doi：10.1007/BF00672031

[37] M. S. Berman and M. M. Som, “Brans-Dicke Models with Time-dependent Cosmological Term,” International Journal of Theory Physics, Vol. 29, 1990, pp. 1411-1414. doi：10.1007/BF00674120

[38] W. Chen and Y. S. Wu, “Implication of a Cosmological Constant Varying as R

[39] E. A. Milne, “Relativity, Gravitation and World structure,” Oxford University Press, Oxford, 1935.

[40] M. S. Berman, M. M. Som and F. M. Gomide, “Brans-Dicke Static Universes,” General Relativity and Gravitation, Vol. 21, 1989, pp. 287-292. doi：10.1007/BF00764101

[41] S. Weinberg, “The Cosmo-logical Constant Problem,” Review Modern Physics, Vol. 61, 1989, pp. 1-23. doi：10.1103/RevModPhys.61.1

[42] T. S. Olson and T. F. Jordan, “Ages of the Universe for Decreasing Cosmological Constants,” Physical Review D, Vol. 35, 1987, pp. 3258-3260. doi:10.1103/PhysRevD.35.3258

[43] O. Bertolami Brans-Dicke, “Cosmology with a Scalar Field Dependent Cosmological Term,” Fortsch Physics, Vol. 34, 1986b, p. 829.

[44] O. Bertolami, “Time-dependence Cosmological Term,” Nuovo Cimento B, Vol. 93, 1986a, pp. 36-42. doi:10.1007/BF02728301

[45] T. L. Chow, “The Variability of the Gravitational Constant,” Nuovo Cimento Lettere, Vol. 31, 1981, pp. 119-120. doi:10.1007/BF02822409

[46] L. S. Levitt, “The Gravitational Constraint at Time Zero,” Nuovo Cimento,Lettere, Serie 2, Vol. 29 , 1980, p. 23.