F(Q) Gravity and its Cosmological Implications

Abstract

This thesis is devoted to study some cosmic aspects within f(Q) gravity in the context of two different models, the power-law model f(Q) = Q + αQ2, λQ0 and the exponential model f(Q) = Qe Q . To complete the target, a homoge nous and isotropic space-time under perfect fluid distribution is considered to develop the dynamical system of equations. We examine the behavior of each model byusing somecosmological parameters including, deceleration parame ter, square speed of sound, statefinder and Om(z)-diagnostic which give results that are compatible with the expanding phenomena of universe. The graphical analysis of square speed of sound justifies the unstability of first model while second model is stable. Using fixed point method, we construct the relevant autonomous system of equations to examine the stability of model for phan tom, vacuum, and non-phantom phases. Moreover the study of growth index of matter perturbation in this theory describes that the anisotropic stress is equal to unity, which is the same result obtained in general relativity