Abstract

A spherically symmetric wormhole family of solutions, with null red-shift, in the context of f(R)-gravity is presented. The model depends on two parameters: m and beta and meets all requirements to be an asymptotically and traversable wormhole. To solve the field equations, an EoS is imposed: p perpendicular to=-rho. It is found that for m=1 the solution satisfies the null energy condition, although F(R)0 everywhere. For m=0, the model satisfies the null energy condition away from the throat, where the function F(R) is everywhere positive and together with dF(R)/dR vanish at the throat of the wormhole. This fact is beyond the scope of the non-existence theorem. Furthermore, the cosmological viability of the model, to address the late - time accelerated epoch, is analyzed on the background of a flat FLRW space-time. The model satisfies consistency of local gravity tests, stability under cosmological perturbations, ghosts free and stability of the de Sitter point.