Dynamical Analysis of Cosmic Evolution in f (R, T ) Theory of Gravity

Abstract

This thesis is mainly focused to investigate the cosmological implications of f(R, T ) theory of gravity considering two distinct models that are, linear f(R, T ) = R + αT , and quadratic in T , f(R, T ) = R + αT 2. The background of flat FRW space-time under perfect fluid distribution is being considered to de- velop the dynamical system of equations. To check the viability of these models and to distinguish between them, we develop important cosmological param- eters including deceleration parameter, square speed of sound, statefinder and Om(z)-diagnostic (in terms of redshift), using obtained solutions. These cosmo- logical parameters give compatible results related to expansion of the universe. The statefinder pair (j, s) for both of these models indicates a rich behavior as it shows different DE eras; phantom, quintessence as well as Chaplygin gas, and also the results for both of these models lie in stable region as shown by graphical analysis of the square speed of sound. We also use fixed points method to describe the stability of the solutions by minimizing the complexity of the field equations. Moreover, we study the growth of matter perturbation for general f(R, T ) theory which discover that the anisotropic stress in this theory is equal to unity, which is the same result as obtained in general relativity. We find that linear f(R, T ) model is close to ΛCDM model but quadratic f(R, T ) model exactly attains ΛCDM limit, so we conclude that the quadratic f(R, T ) is a physically viable model more than that of linear f(R, T ) model.