Finslerian wormholes in squared trace gravity

We investigate traversable wormholes in squared-trace extended gravity within the framework of Finsler-Randers geometry equipped with the Barthel connection. The Einstein-Hilbert action is modified by terms involving the trace of the energy-momentum tensor and its square, generating effective anisotropies through matter-curvature coupling. The resulting field equations are studied under barotropic equations of state with exponential and power-law shape functions. Finslerian anisotropy introduces novel pressure dynamics that enable the classical energy conditions to be satisfied in specific parameter domains. Our analysis quantitatively maps how the Barthel connection scales the parameter space for non-exotic, geometrically viable wormholes compared to purely Riemannian models. These findings suggest that Finslerian modifications provide a powerful mechanism for realizing consistent wormhole structures, offering new perspectives on anisotropic and geometrically enriched space-time configurations in extended gravity.