Quasi-cosmological Traversable Wormholes in $f(R)$ Gravity

In this paper we study traversable wormholes in the context of $f(R)$ gravity. Exact solutions of traversable wormholes are found by imposing the nonconstant Ricci scalar. These solutions asymptotically match spherical, flat and hyperbolic FRW metric. By choosing some static $f(R)$ gravity models, we verify the standard energy conditions for the asymptotically spherical, flat and hyperbolic wormhole solutions. Unlike the Einstein gravity, we find that in the context of $f(R)$ modified gravity, the asymptotically spherical, flat and hyperbolic wormhole solutions can respect the null energy condition (NEC) at the wormhole throat and near that. We find that in some static $f(R)$ models, asymptotically flat and hyperbolic wormholes respect the weak energy condition (WEC) through the whole space.