Analysis of general relativistic hydrodynamic cosmological models with stability factor in theories of gravitation

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.