Constraining the Hybrid Model for Investigating Holographic Dark Energy in Modified Gravity

This study examines the dynamism of holographic dark energy (HDE) in the background of f(R) gravity through a hypersurface-homogeneous space-time setting. Looking at how HDE affects the advancement of the Universe, we used a simplified hybrid expansion law (HEL) to derive a precise solution to the associated field equations. The study begins with the analysis of certain kinematical and physical characteristics related to the model. We applied constraints to the outlined hybrid model using observational Hubble data (OHD), which consists of 32-point data sets, in order to evaluate the model's physical certainty and feasibility. In connection with the values of parameter that show up in our metric, three dynamically potential cosmological scenarios are outlined. Additionally, we examined various energy conditions (ECs) and discerned distinctive cosmic phases through the inspection of statefinder diagnostics and jerk parameter. The squared speed of sound parameter vs2 is used to ensure the model's stability. The study corroborates the Universe's cosmic acceleration, as our findings conform to prevailing observational data, offering viable projections for future research in substantiating HDE.