I Inflation and density perturbations

[Ranku]

Is it possible to estimate the rate of false vacuum decay in the inflationary universe by looking at the density perturbations in the big bang universe?

 

[kimbyd]

Is it possible to estimate the rate of false vacuum decay in the inflationary universe by looking at the density perturbations in the big bang universe?

Maybe, but it's unlikely.

There is the outside possibility that cosmic bubble collisions could be visible in the CMB. Here's a blog post about a paper that looks into this possibility:
https://www.earlyuniverse.org/simulating-cosmic-bubble-collisions-in-full-general-relativity/

So far, there hasn't been a definitive detection of the ring-like structure which would signal such a collision, so there probably won't ever be. If we had gotten lucky and could detect a number of these kinds of collisions, that would place limits on the number of false vacua in our past light cone, which might be useful in determining how often they decay. But with no detection, the answer is that it's probably impossible to know from the CMB data.

 

[bapowell]

Depends. First- or second-order transition?

If the latter, then there is a direct connection between the shape of the potential, i.e. the dynamics of the phase transition, and the characteristics of the density perturbations.