Accelerating the Cosmological Model with Zero-Mass Scalar Field in Lyra’s Geometry
Abstract
Examining Bianchi's type-III cosmological model involves incorporating a zero-mass scalar field in the context of Lyra's geometry. The source of energy-momentum tensor is supposed to be a bulk viscous fluid. A barotropic equation of state is applied to characterize the Pressure and density, seeking a specific solution to the field equations. This solution is derived using the distinctive variation principle for Hubble's parameter proposed by [M.S. Berman, Il Nuovo Cimento B, 74, 182 (1983)]. The ensuing analysis delves into the physical properties inherent in this model.
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References
M.S. Berman, “A Special Law of Variation for Hubble's Parameter,” Il Nuovo Cimento B, 74, 182-186 (1983). http://dx.doi.org/10.1007/BF02721676
A. Einstein, Preussische Akademie der Wissenschaften, Sitzungsberichte, (Berlin, 1915). pp. 831-839.
D. Hilbert, “Nachrichten von der Gesellschaft der Wissenschaftenzu Göttingen,” Math. Phys. Klasse, 3, 395 (1915).
A. Einstein, “The Foundation of the General Theory of Relativity,” Annalen der Physik, 49, 769-822 (1916) http://dx.doi.org/10.1002/andp.19163540702
B. Riemann, Habilitationsschrift, Abhandlungen der Königlichen Gesellschaft der Wissenschaftenzu Göttingen, 13(1), 1854 (1867).
H. Weyl, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin, 465, (1918). https://www.biodiversitylibrary.org/bibliography/42231
G. Lyra, “Über eine Modifikation der Riemannschen Geometrie,” Math. Z. 54, 52-64 (1951). https://doi.org/10.1007/BF01175135
D.K. Sen, “A Static Cosmological Model,” Zeitschriftfur Physik A Hadrons and Nuclei, 149(3), 311-323 (1957).
D.K. Sen, and K.A. Dunn, J. Math. Phys. 12, 578 (1971). https://doi.org/10.1063/1.1665623
W.D. Halford, “Cosmological theory based on Lyra's geometry,” Australian Journal of Physics, 23(5), 863-870 (1970). https://doi.org/10.1071/PH700863
W.D. Halford, “Scalar-tensor theory of gravitation in a Lyra manifold,” J. Math. Phys. 13, 1699–1703, (1972). https://doi.org/10.1063/1.1665894
L. Bianchi, Sugli spazí a tre dimensioni che ammettono un gruppo continuo di movimenti: memoria, vol. 11, (Tipografia della R. Academia dei Lincei, 1898).
D.R.K. Reddy, R. Santhikumar, and T.V. Pradeepkumar, “Bianchi type-III Dark Energy Model in f(R,T) Gravity,” Int. J. Theor. Physics. 52, 1 239 (2013). https://doi.org/10.1007/s10773-012-1325-1
D.R.K. Reddy, R. Santikumar, and R.L. Naidu, “Bianchi type-III cosmological model in f(R, T) theory of gravity,” Astrophys. Space Sci. 342, 249–252 (2012). https://doi.org/10.1007/s10509-012-1158-7
K.S. Adhav, S.D. Katore, R.S. Rane, et al., “Zero mass scalar field with bulk viscous cosmological solutions in Lyra geometry,” Astrophys. Space Sci. 323, 87–90 (2009). https://doi.org/10.1007/s10509-009-0042-6
W.D. Halford, “Cosmological Theory Based on Lyra's Geometry,” Aust. J. Phys. 23, 863-870 (1970). https://doi.org/10.1071/PH700863
G.P. Singh, and K. Desikan, “A new class of cosmological models in Lyra geometry,” Pramana – J. Phys. 49, 205–212 (1997). https://doi.org/10.1007/BF02845856
R.S. Kumar, and B. Satyannarayana, “Accelerating anisotropic cosmological model in f(R, T) theory of gravity,” Indian J. Phys. 91, 1293–1296 (2017). https://doi.org/10.1007/s12648-017-1017-z
S. Rajamahanthi, S. Bora, S.P.S. Komu, et al., “Bianchi-type cosmological models with heat flow in Lyra's geometry,” J. Pure Appl. Math. 7(1), 37-44 (2023). https://doi.org/10.37532/2752-8081.23.7(1).01-09
M. Krishna, S. Koppala, and R.S. Rajamahanthi, “Accelerating plane-symmetric cosmological model with bulk viscous and cosmic Strings in Lyra's geometry,” Indian J. Phys. 98, 3733–3740 (2024). https://doi.org/10.1007/s12648-024-03100-y
C.B. Collins, E.N. Glass, and D.A. Wilkinson, “Exact Spatially Homogeneous Cosmologies,” General Relativity and Gravitation, 12, 805-823 (1980). http://dx.doi.org/10.1007/BF00763057
B. Mishra, P.K. Sahoo, and Ch.B.S. Varma, “Dark Energy Cosmological Model for Bianchi Type III Space-Time with Perfect Fluid,” International Journal of Pure and Applied Mathematics, 99, 1 109-121 (2015). http://dx.doi.org/10.12732/ijpam.v99i1.9
K.P. Singh, and M.R. Mollah, “Bianchi Type III Cosmological Model with Hybrid Scale Factor in the Presence of Van der Waals Fluid in Lyra Manifold,” International Journal of Modern Physics A, 33, 1850207 (2018). https://doi.org/10.1142/S0217751X1850207X
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