The exact solutions of the Einstein field equations for dark energy (DE) in Locally Rotationally Symmetric (LRS) Bianchi type-I metric under the assumption on the anisotropy of the fluid are obtained for exponential volumetric expansion within the frame work of Lyra manifold for uniform and time varying displacement field. The isotropy of the fluid and space is examined.
KeywordsLRS Bianchi Type-I Space-TimePerfect FluidAnisotropic Dark EnergyLyra Geometry
J. A. S. Lima, “Thermodynamics of decaying vacuum cosmologies,” Physical Review D, Vol. 54, No. 4, 1996, pp. 2571-2577. doi:10.1103/PhysRevD.54.2571
S. Perlmutter, et al., “Measurements of Ω and Λ from 42 High-Redshift Supernovae,” The Astrophysical Journal, Vol. 517, No. 2, 1999, pp. 565-586. doi:10.1086/307221
A. G. Reiss, et al., “Observational Evidence from Super- novae for an Accelerating Universe and a Cosmological Constant,” The Astrophysical Journal, Vol. 116, No. 3, 1998, pp. 1009-1038. doi:10.1086/300499
P. de Bernardis, et al., “A Flat Universe from High- Resolution Maps of the Cosmic Microwave Background Radiation,” Nature, Vol. 404, 2000, pp. 955-955. doi:10.1038/35010035
D. N. Spergel, et al., “Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology,” The Astrophysical Journal Supplement Series, Vol. 170, No. 2, 2007, pp. 377-408. doi:10.1086/513700
R. Caldwell and M. Kamionkowski, “The Physics of Cos- mic Acceleration,” Annual Reviews: Nuclear and Particle Science, Vol. 59, 2009, pp. 397-429. doi:10.1146/annurev-nucl-010709-151330
P. J. E. Peebles and B. Rathra, “The Cosmological Con- stant and Dark Energy,” Reviews of Modern Physics, Vol. 75, No. 32, 2003, pp. 559-606. doi:10.1103/RevModPhys.75.559
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
E. Tortora and M. Demianski, “Two Viable Quintessence Models of the Universe: Confrontation of Theoretical Pre- dictions with Observational Data,” Astronomy & Astrophysics, Vol. 431, No. 1, 2005, pp. 27-44. doi:10.1051/0004-6361:20041508
V. F. Cardone, et al., “Some Astrophysical Implications of Dark Matter and Gas Profiles in a New Galaxy Cluster Model,” Astronomy & Astrophysics, Vol. 429, No. 1, 2005, pp. 49-64. doi:10.1051/0004-6361:20040426
R. R. Caldwell, “A Phantom Menace? Cosmological Con- sequences of a Dark Energy Component with Super-Ne- gative Equation of State,” Physics Letters B, Vol. 545, No. 1-2, 2002, pp. 23-29. doi:10.1016/S0370-2693(02)02589-3
P. J. E. Peebles and B. Rathra, “Cosmology with a Time- Variable Cosmological ‘Constant’,” Astrophysical Journal, Part 2 Letters, Vol. 325, No. 2, 1988, pp. L17-L20. doi:10.1086/185100
B. Rathra and P. J. E. Peebles, “Cosmological Conse- quences of a Rolling Homogeneous Scalar Field,” Physical Reviews D, Vol. 37, No.12, 1988, pp. 3406-3427. doi:10.1103/PhysRevD.37.3406
V. Sahni and A. A. Starobinsky, “The Case for a Positive Cosmological Λ-Term,” International Journal of Modern Physics D, Vol. 9, No.4, 2000, pp. 373-443. doi:10.1142/S0218271800000542
Y.-Z. Ma, “Variable cosmological Constant Model: The Reconstruction Equations and Constraints from Current Observational Data,” Nuclear Physics B, Vol. 804, No. 1-2, 2008, pp. 262-285. doi:10.1016/j.nuclphysb.2008.06.019
J. A. S. Lima, et al., “Is the Radiation Temperature- Red- shift Relation of the Standard Cosmology in Accordance with the Data?” Monthly Notices of the Royal Astrono- mical Society, Vol. 312, No. 4, 2000, pp. 747-752. doi:10.1046/j.1365-8711.2000.03172.x
J. A. S. Lima and J. S. Alcaniz, “Angular size in quintess- ence cosmology,” Astronomy & Astrophysics, Vol. 348, No. 1, 1999, pp. 1-5.
T. Koivisto and D. F. Mota, “Accelerating Cosmologies with an Anisotropic Equation of State,” The Astrophysical Journal, Vol. 679, No. 1, 2008, pp. 1-5. doi:10.1086/587451
B. Saha, “Anisotropic Cosmological Models with Perfect Fluid and Dark Energy,” Chinese Journal of Physics, Vol. 43, No. 6, 2005, pp. 1035-1043.
T. Singh and R. Chaubey, “Bianchi Type-I, III, V, VIo and Kantowski-Sachs Universes in Creation-Field Cosmology,” Astrophysics and Space Science, Vol. 321, No. 1, 2009, pp. 5-18. doi:10.1007/s10509-009-9989-6
O. Akarsu and C. B. Kilinc, “Bianchi Type III Models with Anisotropic Dark Energy,” Genenal Relativity and Gravitation, Vol. 42, No. 4, 2010, pp. 763-775. doi:10.1007/s10714-009-0878-7
G. Lyra, “über eine Modifikation der Riemannschen Ge- ometrie,” Mathematische Zeitschrift, Vol. 54, No. 1, 1951, pp. 52-64. doi:10.1007/BF01175135
H. Weyl, “Reine Infinitesimalgeometrie,” Mathematische Zeitschrift, Vol. 2, No. 3-4, 1918, pp. 384-411.
D. K. Sen, “A Static Cosmological Model,” Zeitschrift für Physik A Hadrons and Nuclei, Vol. 149, No. 3, 1957, pp. 311-323.
D. K. Sen and K. A. Dunn, “A Scalar-Tensor Theory of Gravitation in a Modified Riemannian Manifold,” Journal of Mathematical Physics, Vol. 12, No. 4, 1971, pp. 578-287. doi:10.1063/1.1665623
W. D. Halford, “Scalar-Tensor Theory of Gravitation in a Lyra Manifold,” Journal of Mathematical Physics, Vol. 13, No. 11, 1972, pp. 1399-1405. doi:10.1063/1.1665894
M. S. Berman and F. Gomide, “Cosmological Models with Constant Deceleration Parameter,” General Relativity and Gravitation, Vol. 20, No. 2, 1988, pp. 191-198. doi:10.1007/BF00759327
W. D. Halford, “Cosmological Theory Based on Lyra’s Geometry,” Australian Journal of Physics, Vol. 23, No. 4, 1970, pp. 863-869.
D. K. Sen and J. R. Vanstone, “On Weyl and Lyra Manifolds,” Journal of Mathematical Physics, Vol. 13, No. 7 1972, pp. 990-994. doi:10.1063/1.1666099
K. S. Bhamra, “A Cosmological Model of Class One in Lyra’s Manifold,” Australian Journal of Physics, Vol. 27, No. 5, 1974, pp. 541-547.
T. M. Karade and S. M. Borikar, “Thermodynamic Equilibrium of a Gravitating Sphere in Lyra’s Geometry,” General Relativity and Gravitation, Vol. 9, No. 5, 1978, pp. 431-436. doi:10.1007/BF00759843
D. R. K. Reddy and R. Venkateswarlu, “Birkhoff-Type Theorem in the scale-Covariant Theory of Gravitation,” Astronomy & Astrophysics, Vol. 136, No. 1, 1987, pp. 191- 194. doi:10.1007/BF00661267
H. Soleng, “Cosmologies Based on Lyra’s Geometry,” General Relativity and Gravitation, Vol. 19, No. 12, 1987, pp. 1213-1216. doi:10.1007/BF00759100
T. Singh and G. Singh, “Bianchi Type-I Cosmological Models in Lyra’s Geometry,” Journal of Mathematical Physics, Vol. 32, No. 9, 1991, pp. 2456-2459. doi:10.1063/1.529495
G. Singh and K. Desikan, “A New Class of Cosmological Models in Lyra Geometry,” Pramana: Physics and Astro- nomy, Vol. 49, No. 2, 1997, pp. 205-212. doi:10.1007/BF02845856
F. Rahaman, “A Study of an Inhomogeneous Bianchi-I Model in Lyra Geometry,” Astrophysics and Space Science, Vol. 281, No. 3, 2002, pp. 595-600. doi:10.1023/A:1015819414071
F. Rahaman, N. Begum and B. C. Bhui, “Cosmological Models with Negative Constant Deceleration Parameter in Lyra Geometry,” Astrophysics and Space Science, Vol. 299, No. 3, 2005, pp. 211-218. doi:10.1007/s10509-005-5943-4
A. Pradhan, V. K. Yadav and I. Chakrabarty, “Bulk Viscous Frw Cosmology in Lyra Geometry,” International Journal of Modern Physics, Vol. 10, No. 3, 2001, pp. 339-349. doi:10.1142/S0218271801000767
C. P. Singh, “Early Cosmological Models in Lyra’s Geometry,” Astrophysics and Space Science, Vol. 275, No. 4, 2001, pp. 377-383. doi:10.1023/A:1002708316446
C. P. Singh, “Bianchi Type-II Inflationary Models with Constant Deceleration Parameter In General Relativity,” Pramana: Physics and Astronomy, Vol. 68, No. 5, 2007, pp. 707-720.
C. P. Singh, et al., “Bianchi Type-V Perfect Fluid Space- Time Models in General Relativity,” Astrophysics and Space Science, Vol. 315, 2008, pp. 181-189. doi:10.1007/s10509-008-9811-x
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, No. 2, 2004, pp. 665-678. doi:10.1086/383612