False vacuum decay in the de sitter space-time

In the example of the decay of a metastable scalar field state (the conformal vacuum of scalar particles over a false classical vacuum) in the background de Sitter metric, we propose a method to account for the initial quantum field state in the semiclassical calculation of the path integral in a curved space-time. Using this method, we justify the Coleman-De Luccia approach to calculating the decay probability. We interpret the Hawking-Moss instanton as a limit of constrained instantons. We find that the inverse process of the true vacuum going into a false one can occur in the de Sitter space and find the expression for the corresponding probability.