Coleman-de Luccia tunneling wave function

We revisit the famous Coleman-de Luccia formalism for decay of false vacuum in gravitational theory. Since the corresponding wave function is time-independent we argue that its instanton's interpretation as the decay rate probability is problematic. We instead propose that such phenomenon can better be described by the Wheeler-de Witt's wave function. To do so, the Hamilton-Jacobi formalism is employed in the WKB approximation. The scalar and gravitational fields can then be treated as a two-dimensional effective metric. For a particular case of dS-to-dS tunneling, we calculated the wave function and found that it depends only on the potential of the false vacuum. In general, this alternative approach might have significant impact on the study of very early universe and quantum cosmology.