The evolution in curved space-time of quantum fields in theories with relatively flat potentials is considered. It is known that bubble nucleation, a quantum mechanical tunnelling process, may occur in flat space-time even if Ó(ô) has no barrier. It is shown that bubble nucleation can also occur in curved space-time even though there is no bounce solution in the standard formalism for the bubble nucleation rate in curved space-time. Some implications for inflationary scenarios are
discussed.