Rényi Holographic Dark Energy-Inspired Model and Scalar Field Reconstruction in Bianchi Type III Space-Time

In this study, we consider a cosmological model based on Rényi holographic dark energy within the context of an anisotropic Bianchi type III space-time geometry. The dark energy density is taken as a modified function of the Hubble parameter, which enables us to express the Einstein field equations in a closed dynamical system. By solving these equations, we obtain the evolution of the Hubble parameter and examine the main cosmological implications of the model. The physical behavior of the universe is discussed through the analysis of the equation-of-state parameter as well as the deceleration parameter. Our results indicate that the universe evolves from an initial decelerated expansion phase toward a late-time accelerated regime. In the asymptotic limit, the model tends to a de Sitter phase, suggesting the presence of a stable attractor configuration. In addition, we reconstruct the dark energy component in terms of different scalar field frameworks, namely quintessence, tachyon, and k-essence models. The associated scalar fields and their potentials are derived and numerically investigated. The obtained results show a coherent late-time behavior, which is in agreement with the observed accelerated expansion of the universe. The small value of the mean anisotropy parameter indicates that this evolution occurs within a quasi-isotropic Bianchi type III background.