In this paper, we study the cosmological analysis of the modified holographic Ricci dark energy model and reconstruct different scalar field models in the context of Chern-Simons modified gravity. We investigate the deceleration parameter, which shows that the universe is in the accelerating expansion phase. The equation of state parameter in this case also favors the fact that dark energy is the dominant component of universe, which is responsible for the accelerated expansion. A number of scalar fields, such as quintessence, tachyon, K-essence, and dilaton models, are reconstructed using modified holographic Ricci dark energy model in the context of dynamical CS modified gravity. The quintessence and K-essence models represent exponentially increasing behaviors, while tachyon model shows decreasing behavior. Unfortunately, the dilaton model has no numerical solution for modified holographic Ricci dark energy model in the framework of dynamical Chern-Simons modified gravity.

The Sharma–Mittal holographic dark energy model is investigated in this paper using the Chern–Simons modified gravity theory. We investigate several cosmic parameters, including the deceleration, equation of state, square of sound speed, and energy density. According to the deceleration parameter, the universe is in an decelerating and expanding phase known as de Sitter expansion. The Sharma–Mittal HDE model supports a deceleration to acceleration transition that is compatible with the observational data. The EoS depicts the universe’s dominance era through a number of components, such as $\omega =0$, $\frac{1}{3}$, 1, which indicate that the universe is influenced by dust, radiation, and stiff fluid, while $-1<\omega <\frac{1}{3}$, $\omega =-1$, and $\omega <-1$ are conditions for quintessence DE, $\mathrm{\Lambda }$CDM, and Phantom era dominance. Our findings indicate that the universe is in an accelerated expansion phase, and this is similar to the observational data.

We have considered the holographic dark energy and modified holographic Ricci dark energy models to analyze the time-dependent gravitational constant $G\left(t\right)$ and cosmological constant $\Lambda \left(t\right)$ in the context of Chern–Simons modified gravity theory. The FRW metric is used to examine the physical and kinematical properties of these models, which predicted the accelerated expansion phase of universe. Further, the $\Lambda \left(t\right)$ showed increasing trends while $G\left(t\right)$ showed decreasing trends for both cases. Finally, the range $-1.99\times {10}^{-10}{\mathrm{yr}}^{-1}\le \frac{\dot{G}}{G}\le 0$ was estimated mathematically, which is similar to the results obtained from observational data.