Diagnostic Approaches for Interacting generalized holographic Ricci Dark Energy Models

In this paper, we present an analytical solution for the interacting generalized holographic dark energy model, assuming a linear interaction rate between dark energy and dark matter. We determine the equation of state parameter, the generalized holographic Ricci dark energy density, the matter density, and the deceleration parameter. By analyzing the behavior of these cosmological parameters, we demonstrate that our model aligns with recent observations and reproduces the late-time accelerated expansion of the Universe. To compare our model with the $\Lambda$CDM model, we use various diagnostic tools including statefinder, $Om(z)$-diagnostic, statefinder hierarchy, growth rate analysis, and $\omega_H$-$\omega'_H$ plane. We also analyze the stability of the model by examining the speed of sound. These methods show that the dynamics of the Universe remain very close to that of the standard cosmological model.