Cosmic implications of generalized HDE model in FRW universe

In this study, we investigate a generalized holographic dark energy model within the framework of dynamical Chern-Simons modified gravity theory. By incorporating the Hubble parameter H and its higher order derivatives, we explore the equation of state and its implications for the expansion of the known universe using the Friedmann-Robertson-Walker metric. Our analysis reveals three distinct cases arising from the solutions to the Chern-Simons field equations, which depend on the chosen parameters. In the first two cases, we observe confirmation of the accelerated expansion of the universe, consistent with the predicted range of -1 < w < 0. However, in the third case, the depicted behavior exhibits a phantom-like nature. It is important to note that irrespective of the case, the generalized holographic dark energy model supports the transition from deceleration to acceleration, aligning well with observational data. Furthermore, our findings establish that the generalized holographic dark energy model endorses the universe's accelerated expansion within the framework of dynamical Chern-Simons modified gravity theory.