Abstract
In the present paper, we have analyzed the dynamical properties of Einstein’s field equations in cosmology and in the vicinity of Plane symmetric cosmological model. The paper consists of main three parts in Part-I, we investigate the piece of Plane symmetric cosmological model in General Theory of Relativity with Hydrodynamic source. Part-II and Part-III consist the same source and cosmological model in f(R) and f(T) theory of gravity respectively. It is observed that Relativistic Hydrodynamic model in General Theory of Relativity and f(T) gravity is unstable while the model in f(R) gravity is stable. Also, Relativistic Hydrodynamic model in General Theory of Relativity is fully occupied with Quintessence dark energy fluid whereas in f(R) gravity the model shows both matter and dark energy dominated era and remains present in matter dominated era while in f(R) gravity initially it shows standard \( \Lambda \)-Cold Dark Matter model and with the expansion it is fully occupied with quintessence dark energy fluid. Some physical and kinematical properties of the models are also discussed.
Similar content being viewed by others
References
Baojiu, L., Sotiriou, T., Barrow, J.: f(T) Gravity and local lorentz invariance. Phys. Rev. D 83, 064035 (2011)
Baojiu, L., Sotiriou, T., Barrow, J.: Generalizations of teleparallel gravity and local Lorentz symmetry. Phys. Rev. D 83, 104030 (2011)
Berman, M.S., Gomide, F.M.: Cosmological models with constant deceleration parameter. Gen. Relativ. Gravit. 20(2), 191–198 (1988)
Bhoyar, S.R., Chirde, V.R., Shekh, S.H.: Dark energy dominated Bianchi type VI0 Universe with the hybrid expansion law in f(R, T) gravity. Prespacetime J. 8(9), 1101–1112 (2017)
Bhoyar, S.R., Chirde, V.R., Shekh, S.H.: Physical aspects of Bianchi type space–time with quadratic equation of state in f(R) gravity. Prespacetime Journal 7(3), 456–466 (2016)
Bhoyar, S.R., Chirde, V.R., Shekh, S.H.: Stability of accelerating universe with linear equation of state in f(T) gravity using hybrid expansion law. Astrophysics (2017). https://doi.org/10.1007/s10511-017-9480-y
Chirde, V.R., Shekh, S.H.: Anisotropic background for one-dimensional cosmic string in f(T) gravity. Afr. Rev. Phys. 10, 475–484 (2015)
Chirde, V.R., Shekh, S.H.: Barotropic bulk viscous FRW cosmological model in teleparallel gravity. Bulg. J. Phys. 41, 258–273 (2014)
Chirde, V.R., Shekh, S.H.: Cosmological models with magnetized anisotropic dark energy in lyra geometry. Int. J. Adv. Res. 2(6), 1103–1114 (2014)
Chirde, V.R., Shekh, S.H.: Dark energy cosmological model in a modified theory of gravity. Astrophysics 58(1), 121–133 (2015). https://doi.org/10.1007/s10511-015-9369-6
Chirde, V.R., Shekh, S.H.: Interacting two-fluid viscous dark energy models in self creation cosmology. Afr. Rev. Phys. 9, 399–409 (2014)
Chirde, V.R., Shekh, S.H.: LRS Bianchi type-I universe with both deceleration and acceleration in f(R, T) gravity. Prespacetime J. 5(10), 929–942 (2015)
Chirde, V.R., Shekh, S.H.: Plane symmetric dark energy models in the form of wet dark fluid in f(R, T) gravity. J. Astrophys. Astron. 37, 15 (2016)
Chirde, V.R., Shekh, S.H.: Quadratic equation of state with constant deceleration parameter in f(R) gravity. J. Theor. Phys. Cryptogr. 13, 14–19 (2017)
Cunha, J.V.: Kinematic constraints to the transition redshift from supernovae type Ia union data. Phys. Rev. D 79, 047301 (2009)
Cunha, J.V., Lima, J.A.S.: Transition redshift: new kinematic constraints from supernovae. Mon. Not. R. Astron. Soc. 390(1), 210–217 (2008)
Guo, J.-Q., Frolov, A.V.: Cosmological dynamics in f(R) gravity. Phys. Rev. D 88, 124036 (2013)
Katore, S.D., Kapse, D.V.: Dynamics of Bianchi type-VI0 holographic dark energy models in general relativity and Lyra’s geometry. Pramana J. Phys. 88(4), 1–8 (2017)
Kumar, S., Singh, C.P.: Anisotropic Bianchi type-I models with constant deceleration parameter in general relativity. Astrophys. Space Sci. 312(1–2), 57–62 (2007)
Yashiki, Mai: Inflation and cosmological dynamics in f(R) gravity. Phys. Rev. D 96, 103518 (2017)
Mishra, B., Biswa, S.K.: Five dimensional Bianchi type VI0 dark energy cosmological model in general relativity. Afr. Rev. Phys. 9(0012), 77–83 (2014)
Mishra, B., Sahoo, P.K., Ray, P.P.: Accelerating dark energy cosmological model in two fluids with hybrid scale factor. Int. J. Geom. Methods Mod. Phys. 14, 1750124–1750139 (2017)
Mukherjee, A., Banerjee, N.: Acceleration of the universe in f(R) gravity models. Astrophys. Space Sci. 352(2), 893–898 (2014)
Perlmutter, S., et al.: Discovery of a supernova explosion at half the age of the universe and its cosmological implications. Nature 391, 51–54 (1998)
Perlmutter, S., et al.: Measurements of Ω and Λ from 42 high-redshift supernovae. Astrophys. J. 517(2), 565–586 (1999)
Ratra, P.B., Peebles, P.J.E.: Cosmological consequences of a rolling homogeneous scalar field. Phys. Rev. D 37, 3406 (1988)
Riess, A.G., et al.: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009–1038 (1998)
Tripathy, S.K., Mishra, B.: Anisotropic solutions in f(R) gravity. Eur. Phys. J. Plus 131, 273 (2016)
Shamir, M.F., Bhatti, A.A.: Anisotropic dark energy Bianchi type III cosmological models in the Brans–Dicke theory of gravity. Can. J. Phys. 90, 193–198 (2012)
Shamir, M.F.: Some Bianchi type cosmological models in f(R) gravity. Astrophys. Space Sci. 330, 183–189 (2010)
Sharif, M., Yousaf, Z.: Instability of a dissipative restricted non-static axial collapse with shear viscosity in f(R) gravity. J. Cosmol. Astropart. Phys. 06, 19 (2014)
Singh, C.P., et al.: Bianchi type-V perfect fluid space-time models in general relativity. Astrophys. Space Sci. 315, 181 (2018)
Singh C.P., Kumar, P.: Holographic dark energy models with statefinder diagnostic in modified f(R,T) gravity. Gen. Relativ. Quantum Cosmol. (2015). arXiv:1507.07314 [gr-qc]
Shaikh, A.Y., Shaikh, A.S., Wankhade, K.S.: Hypersurface-homogeneous modified holographic Ricci dark energy cosmological model by hybrid expansion law in Saez–Ballester theory of gravitation. J. Astrophys. Astron. 40, 25 (2019). https://doi.org/10.1007/s12036-019-9591-4
Tonry, J., et al.: Cosmological results from high-z supernovae. Astrophys. J. 594, 1–24 (2003)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Shekh, S.H., Chirde, V.R. Analysis of general relativistic hydrodynamic cosmological models with stability factor in theories of gravitation. Gen Relativ Gravit 51, 87 (2019). https://doi.org/10.1007/s10714-019-2565-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10714-019-2565-7