A field theory whose potential contains more than one stable or metastable minimum is considered. It is shown that if the vacuum energies are greater than zero gravitational effects make it possible for bubbles of a higher-energy ‘‘false vacuum’’ to nucleate and expand within a homogeneous region of a lower-energy ‘‘true vacuum.’’ A consequence of this is that in a de Sitter or de Sitter-like space-time any initial state will eventually evolve to a unique statistical mixture of all possible vacua. If the vacuum energies are relatively close, this statistical mixture can be described as a collection of subsystems in thermal equilibrium at the Hawking temperature.

• Received 27 January 1987

DOI:https://doi.org/10.1103/PhysRevD.36.1088