Saez–Ballester gravity in Kantowski–Sachs Universe: A new reconstruction paradigm for Barrow Holographic Dark Energy

We reconstruct Barrow Holographic Dark Energy (BHDE) within the framework of Saez–Ballester Scalar Tensor Theory. As a specific background, we consider a homogeneous and anisotropic Kantowski–Sachs Universe filled up with BHDE and dark matter. By assuming the Hubble radius as an IR cutoff, we investigate both the cases of non-interacting and interacting dark energy scenarios. We analyze the evolutionary behavior of various model parameters, such as skewness parameter, Equation-of-State parameter, deceleration parameter, jerk parameter and squared sound speed. We also draw the trajectories of ωD−ωD′ phase plane and examine statefinder diagnosis. Observational consistency is discussed by inferring the current value of Hubble’s parameter through the best fit curve of data points from Differential Age (DA) and Baryon Acoustic Oscillations (BAO) and commenting on cosmological perturbations and growth rate of matter fluctuations in BHDE. We show that our model satisfactorily retraces the history of the Universe, thus providing a potential candidate explanation for dark energy. Comparison with other reconstructions of BHDE is finally analyzed.