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 scenario based on Tsallis entropy corrections. These entropic formulations modify the cosmological 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 examined. 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 phantom 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
