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

Harpreet  , R. K. Tiwari, H. S. Sahota

Department of Applied Sciences , Sant Baba Bhag Singh Institute of Engineering & Technology, Khiala, Padhiana, Jalandhar- 144030,Punjab, India.

DOI: 10.4236/ojapps.2013.31B1018                

Abstract

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 H2 (where H is Hubble Parameter). 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 decrease. The model does not approach isotropy, if it is small. The model is quasi-isotropic for large value of it.

Keywords

Bianchi Type-I Universe; Varying G and ∧; Cosmology; Hubble Parameter

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. Pradhan and P. Pandey, “Some Bianchi Type I Viscous Fluid Cosmological Models with a Variable Cosmological Constant Astrophys,” 2006, Space Science, Vol. 301, p. 221.
[2]	B. Saha, “Anisotropic Cosmological Models with a Perfect Fluid and a Λ Term,” Astrophysics and Space Science, Vol. 302, No. 1-4, 2006a, pp. 83-91. doi:10.1007/s10509-005-9008-5
[3]	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.
[4]	B. Saha, “Bianchi Type I Universe with Viscous Fluid,” Modern Physics Letters A, Vol. 20, No. 28, 2005a, p. 2127. doi：10.1142/S021773230501830X
[5]	B. Saha, “Anisotropic Cosmological Models with Perfect Fluid and Dark Energy,” Chinese, 2005b.
[6]	R. G. Vishwakarma, “A Model to Explain Varying Λ,G and σ2 Simultaneously,” General Relativity and Gravitation, Vol. 37,2005, pp. 1305-1311. doi：10.1007/s10714-005-0113-0
[7]	S. Carneiro and J. A. S. Lima, “Time Dependent Cosmological Term and Holography,” International Journal of Modern Physics A, Vol. 20, No. 11, 2005, p. 2465. doi：10.1142/S0217751X0502478X
[8]	R. K. Tiwari, “An LRS Bianchi Type–I Cosmological Models with Time Depen-dent L Term,” International Journal of Modern Physics D, Vol. 16, No. 4, 2007, pp. 745-754. doi：10.1142/S0218271807009863
[9]	J. V. Cunha and R. C. Santos, “The Existence of an Old Quasar at z=3.91 and Its Im-plications for λ(t) Deflationary Cosmologies,” International Journal of Modern Physics D, Vol. 13, 2004, p. 1321. doi：10.1142/S0218271804005481
[10]	A. G. Riess, et al., “Type Ia Supernova Discoveries at z > 1 from the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution*,” The Astrophysical Journal, Vol. 607, 2004, p. 665. doi：10.1086/383612
[11]	S. W. Allen, et al., “Constraints on Dark Energy from Chandra Observations of the Largest Relaxed Galaxy Clusters,” Monthly Notices of the Royal Astronomical Society, Vol. 353, No. 2, 2005, pp. 457-467. doi：10.1111/j.1365-2966.2004.08080.x
[12]	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
[13]	T. Padmanabhan, “Cosmological Constant the Weight of the Vacuum,” Physics Reports, Vol. 380, No. 5-6, 2003, pp. 235-320. doi：10.1016/S0370-1573(03)00120-0
[14]	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
[15]	R. G. Vishwakarma, “Study of the Magnitude-Redshift Relation for Type Ia Supernovae in a Model Resulting from a Ricci-Symmetry,” General Relativity and Gravitation, Vol. 33, No. 11, 2001, pp. 1973-1984. doi：10.1023/A:1013051026760
[16]	R. G. Vishwakarma, “A Study of Angular Size-redshift Relation for Models in Which Λ Decays as the Energy Density,” Class Quantum Gravity, Vol. 17, 2000, pp. 38-33. doi：10.1088/0264-9381/17/18/317
[17]	S. Perlmutter, et al., “Measurements of Ω and Λ from 42 High-Redshift Supernovae,” The Astrophysical Journal, Vol. 517, No. 2, 1999, p. 565. doi：10.1086/307221
[18]	I. Arbab, “Bianchi Type I Universe with Variable G and Λ,” General Relativity and Gravitation, Vol. 30, No. 9, 1998, pp. 1401-1405. doi：10.1023/A:1018856625508
[19]	S. Perlmutter, et al., “Discovery of a Supernova Explosion at Half the Age of the Universe,” Nature, Vol. 391 1998, p. 51.
[20]	A. G. Riess, et al., “Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant,” The Astrophysical Journal, Vol. 116, 1998, P. 1009.
[21]	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
[22]	V. Silveira and J. Waga, “Cosmological Poperties of a Class of Λ Decaying Cosmologies,” Physical Revview D, Vol. 56, 1997, p. 4625.
[23]	J. A. S. Lima and M. Trodden, “Decaying Vacuum Energy and Deflationary Cosmology in Open and Closed Universes,” Physical Revview D, Vol. 53, No. 8,1996, pp. 4280-4286. doi：10.1103/PhysRevD.53.4280
[24]	J. A. S. Lima, “Thermodynamics of Decaying Vacuum Cosmologies,”Physical Revview D, Vol. 54, No. 4, 1996, pp. 2571-2577. doi：10.1103/PhysRevD.54.2571
[25]	L. F. B. Torres and I. Waga, “Decaying Lambda Cosmologies and Statistical Properties of Gravitational Lenses,” Monthly Noices of the Royal As-tronomical Society, Vol. 279, No. 3,1996, pp. 712-726. doi：10.1093/mnras/279.3.712
[26]	D. Kalligas, P. S. Wesson and C. W. F. Everitt, “Bianchi type I Cosmological Models with VariableG and Λ: A Comment,” General Relativity and Gravitation, Vol. 27, No. 6, 1995, pp. 645-650. doi：10.1007/BF02108066
[27]	A. I. Arbab and A. M. M. Abdel-Rahaman, “Nonsingular Cosmology with a Time-dependent Cosmological Term,” Physical Revview D, Vol. 50, No. 12,1994, pp. 7725-7728. doi：10.1103/PhysRevD.50.7725
[28]	A. Beesham, “Bianchi Type I Cosmological Models with VariableG and A,” General Relativity and Gravitation , Vol. 26, No. 2,1994, pp. 159-165. doi：10.1007/BF02105151
[29]	J. A. S. Lima and J. M. F. Maia, “Deflationary Cosmology with Decaying Vacuum Energy Density,” Physical Revview D, Vol. 49, No. 10,1994, pp. 5597-5600. doi：10.1103/PhysRevD.49.5597
[30]	J. A. S. Lima and J. C. Carvalho, “Dirac's Cosmology with Varying Cosmological Constant,” General Relativity and Gravitation, Vol. 26, No. 9, pp. 909-916. doi：10.1007/BF02107147
[31]	M. D. Maia and G. S. Silva, “Geometrical Constraints on the Cosmological Constant,” Physical Review D, Vol. 50, No. 12 ,1994, pp. 7233-7238. doi：10.1103/PhysRevD.50.7233
[32]	V. Silveira and J. Waga, “Decaying Λ Cosmologies and Power Spectrum,” Physical Review D. Vol. 50, No. 8,1994, 4890-4894. doi：10.1103/PhysRevD.50.4890
[33]	J. C. Carvalho, J. A. S. Lima and I. Waga, “Cosmological Consequences of a Time-Dependent ΛTerm,” Physical Review D, Vol. 46, No. 6,1992, pp. 2404-2407. doi：10.1103/PhysRevD.46.2404
[34]	D. P. S. Kalligas, Wesson and C. W. F. Everitt, “Flat FRW Models with Variable G and Λ,” General Relativity and Gravitation, Vol. 24, No. 4, 1992, pp. 351-357. doi：10.1007/BF00760411
[35]	M. S. Berman, “Cosmological Models with Variable Gravitational and Cosmological ‘Constants’,” General Relativity and Gravitation, Vol. 23, No. 4,1991a, pp. 465-469. doi：10.1007/BF00756609
[36]	M. S. Berman, “Cosmological Models with Variable Cosmological Term,” Physical Review D, 1991b, pp. 1075-1078.
[37]	D. Pavon, “Nonequilibrium Fluctions in Cosmic Vacuum Decay,” Physical Review D, Vol. 43, No. 2,1991, pp. 375-378. doi：10.1103/PhysRevD.43.375
[38]	Abdel - Rahaman, AMM (1990).A Critical Density Cosmological Model with Varying Gravitation and Cosmological”Constants”General Relativity and Gravitation Vol. 22, No. 6, p. 655.doi：10.1007/BF00755985
[39]	Berman MS, Static Universe in a Modified Brans-Dicke Cosmology. International Journal of Theoretical Physics. Vol. 29, No. 6,1990, pp. 567-570. doi：10.1007/BF00672031
[40]	Berman MS and Som MM Brans-Dicke Models with Time-Dependent Cosmological Term, International Journal of Theoretical Physics , Vol. 29, No. 12,1990, pp. 1411-1414. doi：10.1007/BF00674120
[41]	W. Chen and Y. S. Wu, “Implication of a Cosmological Constant Varying as R-2,” Physical Review D, Vol. 41,1990, p. 695.
[42]	E. A. Milne, “Relativity, Gravitation and World Structure,” Oxford University Press, Oxford ,1935.
[43]	M. S. Berman, M. M. Som and F. M. Gomide, “Brans-Dicke Static Universes,” General Relativity and Gravitation, Vol. 21, No. 3,1989, pp. 287-292. doi：10.1007/BF00764101
[44]	S. Weinberg, “The Cosmological Constant Problem,” Reviews of Modern Physics, Vol. 61, No. 1,1989, pp. 1-23. doi：10.1103/RevModPhys.61.1
[45]	T. S. Olson and T. F. Jordan, “Ages of the Universe for Decreasing Cosmological Constants,” Physical Review D, Vol. 35, 1987, p. 3258.doi：10.1103/PhysRevD.35.3258
[46]	O. Bertolami, “Brans-Dicke Cosmology with a Scalar Field Dependent Cosmological Term,” Fortsch Physicsics, Vol. 34,1986b, p. 829.
[47]	O. Bertolami, “Time-Dependence Cosmological Term,” Nuovo Cimento B, Vol. 93, No. 1,1986a, pp. 36-42. doi：10.1007/BF02728301
[48]	T. L. Chow, “The Variability of the Gravitational Constant,” Nuovo Cimento Lettere, Vol. 31, No. 4, 1981, pp. 119-120. doi：10.1007/BF02822409
[49]	L. S. Levitt, “The Gravitational Constraint at Time Zero,” Nuovo Cimento,Lettere, Vol. 2, No. 29,1980, p. 23.
[50]	V. Silveira and J. Waga, “Decaying Λ Cosmologies and Power Spectrum,” Physical Review D, Vol. 50, No. 8, 1994, pp. 4890-4894. doi：10.1103/PhysRevD.50.4890
[51]	V. Silveira and J. Waga, “Cosmological Properties of a Class of Λ Decaying Cosmologies,” Physical Revview D, Vol. 56, 1997, p. 4625.