Cosmological model in Barrow holographic dark energy with Granda–Oliveros cut-off

This study focuses on the cosmological evolution of Barrow holographic dark energy (BHDE) in a flat FLRW-universe. We take into account a time-dependent scale factor $a(t)={[sinh(kt)]}^{\frac{1}{n}}$, where k and n are positive values, to find the solutions to field equations. This scale factor results in a smooth transition of the universe from its previous decelerating stage to its most recent accelerating stage. Using the Granda–Oliveros cut-off, we examine the chronology of the deceleration parameter, equation of state parameter, and density parameter, and we analyze the positive aspects of the BHDE model. Negative pressure values in this model suggest dark energy dominance, resulting in the universe’s acceleration. We use the statefinder parameters ($r,s$) to improve the accuracy of the results of the dark energy model that is similar to the $\mathrm{\Lambda }$-CDM model.