Cosmographic and phase-space analysis of dynamical Chern–Simons modified and fractal gravities

Abstract

We examine the cosmic scenario of interacting Kaniadakis holographic dark energy in dynamical Chern–Simons modified gravity and the fractal universe. For this purpose, the Hubble, deceleration, coincidence, equation-of-state and jerk parameters have been evaluated in view of the redshift parameter. It is observed that deceleration parameter [Formula: see text] evaluates the accelerated expansion of the universe in both gravities. The coincidence parameter [Formula: see text] exhibits the transition of behavior from dark matter to dark energy era of the universe. The behavior of the equation-of-state parameter [Formula: see text] describes the quintessence and vacuum regions of the universe in both gravities for maximum choices of the interacting parameters. The jerk parameter shows the correspondence of the given model with [Formula: see text]CDM model and other standard models in both gravities. All the parameters exhibit consistent behavior with the Planck 2018 data. We also analyze the dynamical stability in both frameworks by formulating dynamical models in the form of a system of differential equations and evaluating their corresponding critical points. Critical points of both models are stable and phase plots indicate attractor behavior that implies stability of the models. Further, stability conditions of both models signify the accelerating expansion of the universe. In addition, we discuss the thermodynamics of this model with the generalized second law and find its validity in both frameworks.