Maximum Mass < M max < Planck Scale FV Weak Scale FV

would be a ple, if the fact forbidwall false- tunnel to one of the unbound solutions. In the absence probability to go from empty dS to the spacetime of a detailed theory of the nature of these fluctuations, ing an expanding we assume that vacuum the probability bubble of fluctuating is givena by solution the Nucleation Probability of a given mass is given by the exponential of the entropy change due to the change in P ’ CP seed e 2i the area of the 0 Ce S exterior de E Sitter horizon in the presence of a mass [2] : [ ( )] 3 P seed = exp −π − RC 2 , (44) Λ + 11 where R C is the radius of curvature of the cosmological horizon in SdS. Once the bound solution has been fluctuated, it must survive until it reaches the turning point of the classical motion. The authors have shown [1] that any solution with a turning point is unstable against non-spherical perturbations. Even quantum fluctations present on the bubble wall at the time of nucleation will go nonlinear over some range of initial size and mass. To avoid this instability, the seed bubbles must form very near the turning point and be almost spherically symmetric. It is unclear how asphericities will affect the tunneling mechanism discussed in the previous section, but this may be a significant correction to these processes. Assuming that the seed bubble is still reasonable spherically symmetric when it reaches the turning point, the probability to go from empty de Sitter to the spacetime containing an expanding vacuum bubble is given by the