False-vacuum decay in time-dependent and two-field models

We study the false-vacuum decay of a scalar field making use of the functional Schr\"odinger equation. The wave function describing the nucleation and expansion of true-vacuum bubbles is derived to O() and the problem of matching at the classical turning point is discussed. We also study the vacuum decay of a scalar field coupled to a time-dependent external field and derive the traversal time for bubble nucleation. We show that a quasistatic approximation is valid as long as the time scale for the external field to change is long compared to the light-travel time across the bubble. Implications for recently proposed scenarios of first-order inflation are discussed.