Signatures of different dark matter density profiles in constructing traversable wormholes: A theoretical study in Lagrangian-based gravity

Within the framework of matter-geometry coupled gravity, we examine the feasibility of traversable wormholes under different dark matter halos. We utilize the Morris–Thorne spacetime to define the wormhole structure and establish the anisotropic gravitational equations for a specific linear modified model. We derive explicit wormhole geometries supported by anisotropic fluids represented by the pseudo-isothermal, Navarro–Frenk–White, and Bose–Einstein condensation distributions. We show that the chosen parameters enable the built shape functions to satisfy all relevant restrictions. Analyzing the energy conditions, especially the null energy bounds at the wormhole throat, and identifying regions that meet or depart from these requirements are crucial elements of this study. Additionally, we examine a number of significant characteristics, including equilibrium analysis, gravitational mass, complexity factor behavior, embedding diagrams, and the exoticity parameter. Our findings demonstrate that all three wormhole configurations fulfill each of the criteria needed to be satisfied by the underlying gravitational model in this theory.