Achronal cosmic future

The spherically symmetric accretion of dark and phantom energy onto Morris-Thorne wormholes is considered. It is obtained that the accretion of phantom energy leads to a gradual increase of the wormhole throat radius which eventually overtakes the superaccelerated expansion of the Universe and becomes infinite at a time in the future before the occurrence of the big rip singularity. After that time, as it continues accreting phantom energy, the wormhole becomes an Einstein-Rosen bridge whose corresponding mass decreases rapidly and vanishes at the big rip.