A comparative analysis of two cosmological models with time-dependent deceleration parameters and Barrow holographic dark energy in Bianchi type-VI ₀ spacetime

In this study, we examine a spatially homogeneous and anisotropic Bianchi type-VI 0 universe filled with pressureless cold dark matter and Barrow holographic dark energy within the framework of General Relativity. We assume the cold dark matter and the Barrow holographic dark energy to be non-interacting and derive exact solutions to the Einstein field equations by assuming the expansion scalar to be proportional to the shear scalar and considering two distinct time-dependent deceleration parameters, giving rise to two separate cosmological models, referred to as model 1 and model 2. The physical and kinematical behaviours of these models are analyzed using key cosmological quantities such as the Hubble parameter, anisotropy parameter, and equation of state parameter, as well as higher-order cosmographic parameters including jerk, snap, and lerk. Our findings indicate that transition from deceleration to acceleration takes place at z tr = 0.58 for model 1 and at z tr = 0.49 for model 2. The equation of state parameter in both the models lies in the quintessence regime at present, with model 1 tending towards the ΛCDM model and model 2 evolving into the phantom region at later times. Additionally, we examine the validation and violation of the four energy conditions and discuss their implications for these two cosmological models.