Cosmological wormholes in f(R) theories of gravity

Motivated by recent proposals of possible wormhole existence in galactic halos, we analyze the cosmological evolution of wormhole solutions in modified f(R) gravity. We construct a dynamical wormhole that asymptotically approaches a Friedmann-Lemaitre-Robertson-Walker (FLRW) universe, with supporting material going to the perfect isotropic fluid described by the equation of state for a radiation-and matter-dominated universe respectively. Our analysis is based on an approximation of a small wormhole-a wormhole that can be treated as matched with the FLRW metric at some radial coordinate much smaller than the Hubble radius, so that cosmological boundary conditions are satisfied. With a special interest in viable wormhole solutions, we refer to the results of the reconstruction procedure and use f(R) functions which lead to the experimentally confirmed Lambda CDM expansion history of the Universe. Solutions we find imply no need for exotic matter near the throat of considered wormholes, while in the limit of f(R) this need is always present during radiation-and matter-dominated epochs.