Gravitationally dominated instantons and instability of dS, AdS and Minkowski spaces

We study the decay of the false vacuum in the regime where the quantum field theory analysis is not valid, since gravitational effects become important. This happens when the height of the barrier separating the false and the true vacuum is large, and it has implications for the instability of de Sitter, Minkowski and anti-de Sitter vacua. We carry out the calculations for a scalar field with a potential coupled to gravity, and work within the thin-wall approximation, where the bubble wall is thin compared to the size of the bubble. We show that the false de Sitter vacuum is unstable, independently of the height of the potential and the relative depth of the true vacuum compared to the false vacuum. The false Minkowski and anti-de Sitter vacua can be stable despite the existence of a lower energy true vacuum. However, when the relative depth of the true and false vacua exceeds a critical value, which depends on the potential of the false vacuum and the height of the barrier, then the false Minkowski and anti-de Sitter vacua become unstable. We calculate the probability for the decay of the false de Sitter, Minkowski and anti-de Sitter vacua, as a function of the parameters characterizing the field potential.