Wormholes in viable f(R) modified theories of gravity and weak energy condition

In this work wormholes in viable f (R) gravity models are analyzed. We are interested in exact solutions for stress-energy tensor components depending on different shape and redshift functions. Several solutions of gravitational equations for different f (R) models are examined. The solutions found imply no need for exotic material, while this need is implied in the standard general theory of relativity. A simple expression for weak energy condition (WEC) violation near the throat is derived and analyzed. High curvature regime is also discussed, as well as the question of the highest possible values of the Ricci scalar for which the WEC is not violated near the throat, and corresponding functions are calculated for several models. The approach here differs from the one that has been common since no additional assumptions to simplify the equations have been made, and the functions in f (R) models are not considered to be arbitrary functions, but rather a feature of the theory that has to be evaluated on the basis of consistency with observations for the Solar System and cosmological evolution. Therefore in this work we show that the existence of wormholes without exotic matter is not only possible in simple arbitrary f (R) models, but also in models that are in accordance with empirical data.