Cosmological Evolution via Interacting/Non-Interacting Holographic Dark Energy Model for Curved FLRW Space-time in Rastall Gravity

In this work, we explore the phenomenon of cosmic evolution using curved FLRW space-time bounded by apparent horizon with a specific holographic cut-off. To this end, we use the framework of Rastall gravity (RG) and universe is assumed to be consists of interacting/ non-interacting dark energy (DE) and dark matter (DM). In both scenarios, we evaluate exact solutions of the dynamical equations and constraint the holographic parameter $c^2(z)$ assuming a slowly varying function of red-shift during non-interacting model. For interacting model, we consider $c^2$ as a constant function of red-shift. Moreover, we analyze nature of the obtained results via deceleration parameter $(q)$, statefinder pair $(j,s)$ and $Om(z)$-diagnostic by constraining the involved model parameters using latest observational data. The graphical analysis showed that interacting model is very close to $\mathrm{\Lambda }$ cold DM ($\mathrm{\Lambda }$CDM) model as compared to non-interacting case. We conclude that this holographic proposal is enough to describe the cosmic evolution at an accelerating rate.