In this work, we present analytically constructed solutions corresponding to specific shape functions alongside a non-compact matter profile for static and spherically symmetric traversable wormholes (Formula: see text) within the framework of the well-known Formula: see text gravity theory. An extensive analysis of Formula: see text gravity is carried out, demonstrating its viability as an alternative to general relativity. We derive subclasses of exact solutions to the modified gravitational field equations with respect to two feasible choices of shape function, namely Formula: see text and Formula: see text, along with a suitable matter density profile under the cosmologically consistent linear model Formula: see text. The associated free parameters are sufficiently constrained to investigate distinct models of traversable Formula: see text. In this framework, we investigate the physical reliability and internal behavior of the proposed spacetime geometries by examining various energy conditions. The results indicate the non-singularity and regularity of the solutions, except for the radial null energy condition and the tangential dominant energy condition, which are violated in the first two cases. The credibility of the models is evaluated by the pressure anisotropy, which exhibits attractive behavior in the first case and repulsive behavior in the last two cases. Moreover, the viability of the spacetime solutions is examined through the consistency of Herrera’s criteria. Finally, these results provide valuable insight into the possible behavior of spacetime in strong-field regimes and may contribute to the development of more realistic models of compact objects in alternative theories of gravity.
Bukhari et al. (2026) studied this question.