Evolving Lorentzian wormholes supported by phantom matter and cosmological constant

In this paper we study the possibility of sustaining an evolving wormhole via exotic matter made of phantom energy in the presence of a cosmological constant. We derive analytical evolving wormhole geometries by supposing that the radial tension of the phantom matter, which is negative to the radial pressure, and the pressure measured in the tangential directions have barotropic equations of state with constant state parameters. In this case the presence of a cosmological constant ensures accelerated expansion of the wormhole configurations. More specifically, for positive cosmological constant we have wormholes which expand forever and, for negative cosmological constant we have wormholes which expand to a maximum value and then recolapse. At spatial infinity the energy density and the pressures of the anisotropic phantom matter threading the wormholes vanish; thus these evolving wormholes are asymptotically vacuum $\Lambda$-Friedmann models with either open or closed or flat topologies.