Where this parameter is rather than tunneling suddenly is very slowly evolving, and then sinking into the true vacuum and then subject to damped oscillations, which is how it re-heats the universe. new inflation had it's own issues. an improved version or a modified version with other features and problems called chaotic inflation, was proposed where the phase transition is gone alltogether and quantum fluctuations play the role of moving the field away from the actual vacuum whence it slowly rolls, and this occurs locally. 