Wormholes practicable in a cosmological background

For a Morris-Thorne wormhole in a cosmological background we analize the embedding surfaces and deduce an expression for the proper radial distance taking a conformal factor Ω = 1. Further, given the existence of an exotic material (negative energy density), the conditions to have a traversable wormhole are studied taking into account a cosmological background with a time dependent conformal factor Ω. Additionally, the exoticity condition is calculated together with the energy density as measured by a traveler across the wormhole.