Barrow Holographic Dark Energy Model in Bianchi Type-III Universe with Quintessence

In this paper, we study a spatially homogeneous and anisotropic Bianchi type-III universe containing cold dark matter and Barrow holographic dark energy within the framework of General Relativity. We assume the cold dark matter and Barrow holographic dark energy to be non-interacting and obtain exact solutions of the Einstein field equations by considering a hybrid expansion law and assuming that the expansion scalar is proportional to the shear scalar. We examine the physical and kinematical properties of the resulting model using parameters such as the Hubble parameter, the anisotropic parameter, the deceleration parameter, the equation of state parameter, the jerk parameter etc. We also examine whether the energy conditions are violated or validated. We find that the Null, Weak, and Dominant energy conditions are fulfilled, while the Strong Energy Condition is violated, which supports the accelerated expansion of the universe. The Statefinder diagnostics have been conducted based on recent cosmological observations. In addition, wereformulated the correspondence between quintessence scalar field and Barrow holographic dark energy model.