Dynamical Stability of Modified Friedmann Equation Through Non-Linear Interactions

Abstract

In this thesis, we discuss the dynamical stability scenario in the framework of dynamical Chern-Simons modified theory of gravity. In this regards, we develop six models with nonlinear interactions in the theoretical framework of dynamical Chern-Simons modified gravity and apply the dynamical system analysis to investigate their dynamical stability with phase portraits. These nonlinear interactions are considered through energy conser- vation equations between dark energy and dark matter. We find the dynamical system in terms of autonomous system of differential equations of fractional energy densities of dark energy and dark matter with respect to e-fold number of the universe. This system of equa- tions depends on equation of state parameters related to matter and dark energy and yields the critical points for each interacting model. We consider three cases for matter equation of state as radiation, pressure-less, stiff fluid with various values of dark energy equation of state parameter representing current accelerated expansion of the universe and specific value of interaction parameter. The eigenvalues at each critical point are evaluated and the stability is verified by signs of eigen values. Furthermore, the attractor behavior for sta- ble critical point and repulser behavior for unstable state are discussed through the phase portrait analysis.