Phase Space Analysis and Cosmic Parameters of Dynamical Dark Energy Model

Abstract

This thesis explores the stability analysis of Friedmann-like spacetimes using dynamical system methods. For this purpose, we begin by considering a modified cosmological sce nario based on Tsallis entropy corrections. These entropic formulations modify the cosmo logical field equations that govern the universe’s dynamics. We incorporate these modified Friedmann equations and convert them into a first-order autonomous system of differential equations. To identify the system’s equilibrium points, we consider the interaction between cosmological fluids. Various linear and non-linear forms of interaction models are exam ined. For each model, we calculate the critical points and discuss their behavior associated with eigenvalues. We investigate the different stages in the universe’s evolution including dust and radiation dominated era of the universe as well as quintessence, ΛCDM and phan tom regimes. In addition, we develop the phase space portraits of all the interaction models revealing the stable, unstable and saddle behavior of critical points. In most of the cases, the system supports stable critical points.