Vacuum decay is a prominent example of strongly nonlinear
effects in quantum field theory with potentially important
implications for cosmology, relating to phase transitions in the early
universe or the supposed metastability of the current Higgs vacuum.
Although a general theoretical description was laid out in the 80s by
Sidney Coleman and his collaborators, fundamental questions pertaining
to the back-reaction of true vacuum bubbles on space-time curvature
and their correlations remain so far unanswered, calling for different
approaches to the problem. In this talk, after a brief review of
Coleman’s theory emphasizing its genericness and limitations, I will
present a recently-proposed cold-atoms model in which some of these
ideas could be tested in laboratory experiments. I will discuss the
mathematical correspondence between the two problems and focus on how
a localized defect changes the decay rate, taking the example of a
vortex in a Bose-Einstein condensate and comparing with the effect of
a black hole in a relativistic theory.