Cosmic implications of Kaniadakis HDE model in Chern-Simons modified gravity

In this study, we investigate the FRW model in the Chern–Simons modified gravity framework, considering holographic dark energy and Kaniadakis holographic dark energy models. Employing the field equation of Chern–Simons gravity, it is analyzed some important cosmological parameters such as density, equation of state, and deceleration parameters for both models. Our findings, presented visually through graphs, reveal that holographic dark energy places the equation of state within $\omega \in (-1,-0.4)$, while Kaniadakis holographic dark energy spans $\omega \in (-0.8,-0.4)$. These results demonstrate the dynamic nature of dark energy’s influence. Our study highlights the interplay of quintessence and $\Lambda \mathrm{CDM}$ across cosmic eras. We identify the ranges of $q\in (-0.89,-0.86)$ and $q\in (-0.9925,-0.9922)$ for Kaniadakis holographic dark energy and holographic dark energy, offering insights into their roles in cosmic inflation which implies that the universe attributes are impacted by both quintessence and the $\Lambda$CDM model in Chern–Simons modified gravity. In addition, this study implies that the universe’s expansion is decelerating in its current state.