We investigate a cosmological scenario based on the power–law entropy–corrected holographic dark energy (PLECHDE) model combined with a normalized cubic parametrization of the Hubble expansion rate. The framework incorporates quantum–gravity–motivated corrections to the horizon entropy while retaining a flexible, data driven description of the cosmic expansion history. The model is formulated in a spatially flat FLRW background, and the resulting dynamical and geometrical quantities including the dark-energy density, pressure, equation of state, deceleration parameter, and statefinder diagnostics are derived and analyzed. To constrain the free parameters of the model, we perform a comprehensive statistical analysis using observational Hubble data from cosmic chronometers (OHD), DESI measurements, and the Pantheon + compilation of Type Ia supernovae. From the joint OHD + DESI DR2 + Pantheon + dataset, we obtain the best-fit values H 0 = 73 . 15 − 0.20 + 0.21 km/s/Mpc, α = 1 . 75 − 0.28 + 0.29 , β = − 0 . 75 − 0.21 + 0.21 , and γ = 0 . 64 − 0.07 + 0.07 with the entropy correction parameter constrained within the consistent range δ > 2. The joint analysis yields a slightly lower χ min 2 compared to the standard ΛCDM model and negative values of ΔAIC and ΔBIC, indicating a mild statistical preference for the proposed model. The cosmological evolution exhibits a smooth transition from a matter-dominated decelerated phase to a late-time accelerated expansion, with the transition redshift lying in the observationally consistent range 0.5 ≲ z t ≲ 0.7. Overall, our results demonstrate that the PLECHDE model with a cubic Hubble parametrization provides a physically consistent and observationally viable description of late time cosmic acceleration, with entropy corrections introducing controlled deviations that can be tested by future high precision cosmological surveys.
Yadav et al. (Sun,) studied this question.