Exploring Wormholes in Non-linear f(R,ℒm) Gravity with Dekel-Zhao Dark Matter Profile

In this work, we investigate tidal-less wormhole geometries within the framework of [Formula: see text] gravity, incorporating the effects of the Dekel-Zhao (DZ) dark matter halo, which follows a double power-law density profile. We consider a non-linear gravitational model given by [Formula: see text], where [Formula: see text] is a free parameter, and derive the corresponding modified field equations. Wormhole solutions are obtained by embedding the DZ dark matter distribution into the geometry. We analyze key physical characteristics including energy conditions, equation of state parameters, and equilibrium criteria, with a focus on the stability of the configuration via the Tolman-Oppenheimer-Volkoff (TOV) equation. Notably, the inner slope parameter [Formula: see text] of the DZ profile significantly influences the throat radius and internal force balance. Our results indicate that the presence of DZ dark matter reduces the amount of exotic matter around the wormhole throat, as quantified by the Volume Integral Quantifier (VIQ), thereby enhancing the physical plausibility of the wormhole solutions within this modified gravity framework.