Motivated by a recently proposed "extended" inflation scenario, we apply the formalism of Coleman and De Luccia to the false-vacuum decay of a scalar field coupled to a scalar-tensor theory of gravity. In particular, we discuss a model for false-vacuum decay of a scalar field $\sigma$ minimally coupled in a Brans-Dicke-like theory of gravity. In such theories, the effective gravitational constant is a function of a scalar field $\phi$. In general, $\phi$ will have nontrivial dynamics in the false vacuum, and as $\phi$ varies the decay rate of the $\sigma$ false vacuum need not be constant. We present both an explicit "thin-wall" calculation of the decay rate, and a more general numerical "thick-wall" calculation, comparing them to the standard results for Einstein gravity. We consider some questions of principle concerning boundary conditions for the $\phi$ field. We discuss the consequences of these results for extended models of inflation.

• Received 17 November 1989

DOI:https://doi.org/10.1103/PhysRevD.41.3024