Accelerating Anisotropic Bianchi Type-V Model with Barotropic Matter and Viscous Dark Energy in Lyra Geometry

V.G.Mete; A.S. Bansod; P.B.Murade

doi:https://doi.org/10.14445/22315373/IJMTT-V66I11P510

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 11 | Year 2020 | Article Id. IJMTT-V66I11P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I11P510

Accelerating Anisotropic Bianchi Type-V Model with Barotropic Matter and Viscous Dark Energy in Lyra Geometry

V.G.Mete, A.S. Bansod, P.B.Murade

Abstract

The present study deals with spatially homogeneous and anisotropic Bianchi type-V universe filled with barotropic matter and viscous dark energy in Lyra geometry. To get the solutions of the field equations, we consider the hybrid expansion law (HEL) for the average scale factor proposed by Akarsu et al. [69]. To differentiate between different dark energy models, we perform a geometrical diagnostic with the help of statefinder pair },{sr . The physical and geometrical behaviors of the model are studied in detail.

Keywords

Bianchi types-V metric, viscous dark energy, statefinder parameters, Lyra geometry

References

[1] A.G.Riess, et al. “Observational evidence from supernovae for an accelerating universe and a cosmological constant”, Astron.J.vol.116, pp.1009–1038,May1998.
[2] S. Perlmutter, et al. “Measurements of Ω and Λ from 42 high-redshift Supernovae”, Astrophys. J., vol.517, pp.565-586, June 1999.
[3] A. D. Miller, et al., “A measurement of the Angular Power Spectrum of the Cosmic Microwave background from l=100 to 400”, The Astrophysical Journal, vol. 524,pp. L1–L4,Oct.1999.
[4] A. Benoit, et al.-Cosmological constraints from Archeops, Astronomy and Astrophysics.,vol.399,pp.L25-L30,March,2003.
[5] S. T. Myers ,C.R. Contaldi and J.R. Bond et al. “A Fast Gridded Method For The Estimation of The Power Spectrum of The Cosmic Microwave Background From Interferometer Data With Application to The Cosmic Background Imager”, Astrophys. J., vol. 591, pp.575-598,July 2003.
[6] L. Page, et al., “First-year wilkinson microwave anisotropy probe (wmap)1observations:interpretation of the TT and TE angular power spectrum peaks”, Astrophys. J. Suppl. Ser.,vol. 148, pp.233-241,May 2003.
[7] D.N.Spergel, L. Verde, H.V. Peiris, E. Komatsu, M.R. Nolta, C.L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S.S. Meyer, L. Page, G.S. Tucker, J.L. Weiland, E. Wollack and E.L.Wright, “First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters”. The Astrophysical Journal Supplement Series, vol. 148, pp.175-194,May 2003.
[8] M. Tegmark, et al., “Cosmological parameters from SDSS and WMAP”, Phys. Rev. D, vol. 69, 103501,May 2004.
[9] Y. Aditya, R.L. Naidu, D.R.K. Reddy, “Non-vacuum plane symmetric universe in f(R) gravity”, Results in Physics,vol.12,pp.339-343, March 2019.
[10] B. Ratra, P.J.E. Peebles, “Cosmological consequences of a rolling homogeneous scalar field”, Phys. Rev. D,Vol.37, pp. 3406-3427,June 1988.
[11] C. Wetterich, “Cosmology and the fate of dilatation symmetry”, Nuclear Physics B, Vol. 302,pp.668-696,June 1988.
[12] B. Feng, X.L.Wang, X . Zhang, “Dark Energy Constraints from the Cosmic Age and Supernova”, Phys. Lett. B, vol.607, pp.35, 2005.
[13] R. R. Caldwell, “phantom menace? Cosmological consequences of a dark energy component with super-negative equation of the state”, Phys. Lett. B, vol. 545, pp.23,2002.
[14] M. C. Bento, O. Bertolami, A.A. Sen, “Generalized chaplygin gas, accelerated expansion, and dark-energy-Matter unification”, Phys. Rev. D, vol. 66, 043507, 2002.
[15] O. Bertolami , F. Gil Pedro , M. Le. Delliou ,”Dark Energy-Dark Matter Interaction and putative violation of the Equivalence Principle from the Abell Cluster A586”, Phys. Lett.B,vol.654,pp.165,2007.
[16] S.K. Srivastava, “Future Universe With w(-1 Without Big Smash”, Phys. Lett. B,vol. 619,pp.1-4,July 2005.
[17] L. Perivolaropoulos, “Accelerating Universe: Observational and Theoretical Implication”, AIP Conf. Proc. Vol.848, pp.698-712, Sep.2006.
[18] E.J. Copeland, M. Sami, S. Tsujikawa, “Dynamics of the dark energy”, International Journal of Modern Physics D,vol.15,No.11, pp.1753-1935,Nov.2006.
[19] E. Komatsu, J. Dunkley, et al., “Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation”, Astrophys. J. Suppl. Ser.vol. 180, pp. 330, 2009.
[20] G. Hinshaw, et al., “Five-Year Wilkinson Microwave Anisotropy Probe Observations: Data Processing, Sky Maps, and Basic Results”, Astrophys. J. Suppl. Ser. Vol.180, pp. 225, 2009.
[21] R.R. Caldwell, M. Kamionkowski, N.N. Weinberg, “Phantom Energy: Dark Energy with w(−1 Causes a Cosmic Doomsday”, Phys. Rev. Lett. Vol.91, 071301, 2003.
[22] S. Nesseris, L. Perivolaropoulos,”Fate of bound systems in phantom and quintessence Cosmologies”, Phys. Rev. D,vol.70, 123529,2004.
[23] S.M. Carroll, M. Hoffman, M. Trodden, “Can the dark energy equation-of-state parameter w be less than−1?”, Phys. Rev. D ,vol.68, 023509 ,2003.
[24] C.J. Feng, X. Zhou, “Viscous Ricci dark energy”, Phys. Lett. B ,vol. 680, pp.355-358,2009.
[25] J.D. Barrow “Sudden Future Singularities”, Class. Quantum Gravity, vol. 21, L79 ,2004.
[26] T.R. Jaffe, A.J. Banday, H.K. Eriksen, K.M. Gòrski, F.K. Hansen, “Evidence of vorticity and shear at large angular scales in the WMA data: a violation of cosmological isotropy?”, Astrophys. J. vol.629, L1,2005.
[27] W.D. Zimdahl, J. Schwarz, A.B. Balakin and D. Pavón, “Cosmic antifriction and accelerated expansion”, Phys. Rev. D, vol. 64, 063501, 2001.
[28] A.B. Balakin, D. Pavón, D.J. Schwarz, W. Zimdahl, “Curvature force and dark Energy”, New J. Phys., vol.5,pp.85 ,2003.
[29] T. Padmanabhan, S. Chitre, “Viscous universes”, Phys. Lett. A , vol.120,pp. 433,1987.
[30] M. Cataldo, N. Cruz, S. Lepe, “Viscous dark energy and phantom evolution”, Phys. Lett. B ,vol. 619, 5 ,2005.
[31] I. Brevik, O. Gorbunova, “Dark energy and viscous cosmology”, Gen. Relativ. Gravit., vol. 37, 2039,2005.
[32] M. Szydlowski, O. Hrycyna, “Dissipative or conservative cosmology with dark energy?”, Ann. Phys., vol. 322, 2745 ,2007.
[33] C.P. Singh, “Bulk viscous cosmology in early Universe”, Pramana J. Phys., vol. 71, 33,2008.
[34] H. Amirhashchi, “Interacting viscous dark energy in a Bianchi type-III universe”, Res. Astron. Astrophys, vol.14, 1121,2014.
[35] H. Amirhashchi, “Interacting viscous dark energy in Bianchi type-I universe”, Astrophys. Space Sci., Vol. 351,pp.641-649,2014.
[36] H. Amirhashchi , “Viscous dark energy in Bianchi type-V space-time”, Phys. Rev. D ,vol.96,123507, 2017.
[37] A. Sheykhi, M.R. Setare, “Interacting New Agegraphic Viscous Dark Energy with Varying G”, Mod. Phys. Lett. A ,vol.26,pp.1897,2 2011.
[38] R.L. Naidu, “Bianchi type-II modified holographic Ricci dark energy cosmological model in the presence of massive scalar field”, Can. J. Phys.,vol. 97, pp.330-336 ,2019.
[39] E.Sheykhi, E. Ebrahimi and Y. Yousefi, “Generalized ghost dark energy in Brans–Dicke theory”, Can. J. Phys.,vol.91,pp.662-667,2013.
[40] V.Fayaz, H. Hossienkhani, A. Pasqua, Z. Zarei and M. Ganji, ”Anisotropic universe and generalized ghost dark energy in Brans–Dicke Theory”, Can. J. Phys., vol. 94, pp.201-208 ,2016.
[41] M.P.V.V. Bhaskar Rao, D.R.K. Reddy, and K.S. Babu, ”A modified holographic Ricci dark energy model in a self-creation cosmology” Can. J. Phys. Vol.94, pp.1314-1318 ,2016.
[42] D.R.K.Reddy, S. Anitha and S. Umadevi, “Holographic dark energy model in Bianchi type VI0 Universe in a scalar–tensor theory of gravitation with hybrid expansion law”, Can. J. Phys. Vo.94, pp.1338-1343,2016.
[43] M.V. Santhi, V.U.M. Rao, Y. Aditya, “Bianchi type-VI0 modified holographic Ricci dark energy model in a scalar–tensor theory”, Can. J. Phys. Vol.95, pp.179-183 ,2017.
[44] M.P.V.V. Bhaskar Rao, D.R.K.Reddy and K.S. Babu, “Kantowski–Sachs modified holographic Ricci dark energy model in Saez–Ballester theory of gravitation”, Can. J. Phys.vol. 96, pp.555-559,2018.
[45] W.D.Halford,”Cosmological theory based on Lyra’s geometry”, Aust.J.Phys.,vol.23, pp.863,1970.
[46] H.H. Soleng, “Cosmologies based on Lyra’s geometry”, Gen.Relativ.Gravit.,vol.19,pp.1213,1987.
[47] H. Weyl,-"Reine Infinitesimal Geometrie.", Mathematische Zeitschrift, vol.2, pp.384-411,1918.
[48] G. Lyra, “Übereine Modifikation der Riemannschen Geometrie”, Mathematische Zeitschrift.vol.54, pp.52-64,1951.
[49] D.K. Sen, K.A. Dunn, “A Scalar-Tensor Theory of Gravitation in a Modified Riemannian Manifold”, J. Math. Phys.,vol.12 ,pp.578,1971.
[50] D.K. Sen, “A Static Cosmological Model”, Z. Phys. Hadrons Nucl.,vol.149, pp.311,1957
[51] H.H. Soleng ,”Self-creation cosmological solution”, Astrophys. Space Sci.,vol. 139 ,pp.13,1987.
[52] R.M. Gad, “Axially symmetric cosmological mesonic stiff fluid models in Lyra’s geometry”, Can. J. Phys.,vol. 89, pp.773-778 ,2011.
[53] K.S. Adhav, “LRS Bianchi Type-I Universe with Anisotropic Dark Energy in Lyra Geometry”. Int. J. Astron. Astrophys.,vol.1, pp.204, 2011.
[54] A. Pradhan, A.K.Singh, ”Anisotropic Bianchi Type-I String Cosmological Models in Normal Gauge for Lyra’s Manifold with Constant Deceleration Parameter”, International Journal of Theoretical Physics,vol. 50, pp.916-933,2011.
[55] S.D.Katore, S. P. Hatkar “Kaluza Klein universe with magnetized anisotropic dark energy in general relativity and Lyra manifold”, New Astronomy,vol.34,pp. 172,2015.
[56] S.Ram, S. Chandel,S., M.K. Verma, “Hypersurface-homogeneous cosmological models with dynamical equation of state parameter in Lyra geometry”, Canadian J. Phys.,vol. 93,pp.1100 ,2015.
[57] S. Ram, S. Chandel, S., M.K. Verma, “Kantowski- Sachs universe with anisotropic dark energy in Lyra geometry”, Chin. J. Phys., vol.54,pp.953,2016.
[58] K.P. Singh, M.R. Mollah, “Could the Lyra manifold be the hidden source of the dark energy?”, Int. J. of Geom. Meth. in Mod. Phys. vol.14, 1750063,2017.
[59] M. Abdel-Megied and E. Hegazy,”Bianchi type VI cosmological model with electromagnetic field in Lyra geometry”, Can. J. of Phys. Vol.94, pp.992-1000 ,2016.
[60] H. Caglar, S. Aygun, “Exact solutions of bulk viscous with string cloud attached to strange quark matter for higher dimensional FRW universe in Lyra geometry”, AIP Conference Proceedings, vol. 1722,050001,2016.
[61] H. Moradpour, A.S. Jahromi, “Static traversable wormholes in Lyra manifold”, Int. J.Mod. Phys. D,vol. 27, 1850024 ,2017.
[62] W.D.R. Jesus,A.F. Santos, “On causality violation in Lyra Geometry “,Int. J.Geom. Meth.Mod.Phys.,vol. 15, no.08, 1850143,2018.
[63] R.N. Patra, A.K. Sethi, B. Nayak, “Effect of dark energy on cosmological parameters with LVDP in Lyra manifold”, New Astron. vol.66,pp.74-78,2019.
[64] V.P. Kadam, “Holographic Dark Energy Model in Brans-Dicke Theory of Gravitation”, Int.J. of Mathematics Trends and Technology, vol.65,Issue 12, pp.62-69 ,Dec.2019.
[65] V.U., Edlabadkar, G.S. Khadekar, R. Raddha “Behaviour of Strange Quark Matter with Domain Walls in 5D Kaluza-Klein Theory of Gravitation “, Int.J. of Mathematics Trends and Technology, Vol.65,Issue 5, pp.52-64 , May 2019.
[66] Mantu Kumar, “Hyperface Homogeneous Cosmological Models with Stiff-Matter in General Relativity”, Int.J. of Mathematics Trends and Technology, Vol.65,Issue 5,pp.143-148, May 2019.
[67] C.Eckart, “The Thermodynamics of Irreversible Processes. III. Relativistic Theory of the Simple Fluid”, Phys. Rev. vol.58, pp.919 ,1940.
[68] S. Nojiri, S. D. Odinstov, “Quantum desitter cosmology and phantom matter”, Phys. Lett. B, vol.562,pp.147,2003.
[69] O. Akarsu, T. Dereli,”Cosmological models with linearly varying deceleration parameter”, Int. J. Theor.Phys.vol.51, pp.612,2012.
[70] V.Sahni, T.D. Saini, A.A. Starobinsky and U. Alam, “Statefinder -- a new geometrical diagnostic of dark energy”, JETP Lett.Vol.77, pp.201-206,2003.
[71] U. Alam, V. Sahni, T.D. Saini, A.A. Starobinsky, “Exploring the expanding universe and dark energy using the statefinder Diagnostic”, Mon. Not. R. Astron. Soc., vol. 344, pp.1057-1074,Sept.2003.
[72] Z.K. Guo, N. Ohta, S. Tsujikawa, “Probing the coupling between dark components of the universe”, Phys.Rev.D.,vol. 76, 023508,2007.
[73] G.R.Farrar, P.J.E. Peebles, “Interacting dark matter and dark energy”, Astrophys. J. vol.604,1 ,2004.
[74] Amendola , “Acceleration at z>1?”, Mon. Not. R. Astron. Soc. ,vol.342, pp.221,2003.
[75] P.A.R.Ade, et. al.,”Plank 2013 results XVI cosmological parameters”, Astro. and Astrophys. ,vol.571, pp.66,2014.
[76] A.G.Riess, L. G. Strolger, et al., “Type Ia Supernovae Discoveries at from the Hubble Space Telescope:Evidence for Past Deceleration and Constraints on Dark Energy Evolution”, Astrophys. J. ,vol.607, pp.665, 2004.
[77] P. Astier, J. Guy, N. Regnault, R. Pain, E. Aubourg, et. al., “The Supernova Legacy Survey: measurement of ΩM, Ω Λ and from first year data set”, Astron. and Astrophys,vol.447,pp.31,2006.
[78] D.J. Eisenstein, I. Zehavi ,D.W. Hogg, et. al., “Detection of baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies”, The Astrophys. J. , vol.633,pp.560, 2005.

Citation :

V.G.Mete, A.S. Bansod, P.B.Murade, "Accelerating Anisotropic Bianchi Type-V Model with Barotropic Matter and Viscous Dark Energy in Lyra Geometry," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 11, pp. 117-127, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I11P510