Power-Law Corrected Holographic Dark Energy through Barrow Entropy

We investigate a power-law corrected Barrow Holographic Dark Energy (BHDE) model in a flat Friedmann-Lemaître-Robertson-Walker (FLRW) Universe. The model incorporates quantum gravitational corrections to the Barrow entropy and introduces additional free parameters beyond the standard BHDE framework. These parameters are constrained using a joint analysis of Cosmic Chronometer (CC), Baryon Acoustic Oscillation (BAO) datasets through Markov Chain Monte Carlo (MCMC) techniques. The predicted Hubble expansion history shows good agreement with observational data and the [Formula: see text]CDM model. Cosmological diagnostics, including the equation of state parameter, deceleration parameter, jerk, snap, Statefinder pair [Formula: see text], and the [Formula: see text]-[Formula: see text] plane, with the model evolving toward the [Formula: see text]CDM limit at late times and exhibiting freezing behavior. Furthermore, the Generalized Second Law of thermodynamics is found to hold on the apparent horizon throughout cosmic evolution. These results demonstrate that the power-law corrected BHDE model is a viable and thermodynamically consistent model for accounting for the observed accelerated expansion of the Universe at late times.