Dynamics and observational constraints on Tsallis holographic dark energy in Bianchi type-III universe within Lyra geometry

This paper explores a cosmological model based on Tsallis holographic dark energy within Lyra geometry for an anisotropic Bianchi type-III universe. We assume a proportional relation between expansion and shear scalar; exact solutions of the modified gravitational field equations are obtained. The model parameters are constrained using observational Hubble data, showing consistency with present cosmological measurements. The results indicate a smooth transition from early decelerated expansion to late-time acceleration driven by dark energy. The evolution of energy densities and the equation-of-state parameter support a stable quintessence-like behaviour, while energy condition analysis confirms the physical viability of the model. Additional cosmographic diagnostics further demonstrate that the framework provides a consistent description of cosmic evolution beyond the standard cosmological scenario.