How does Nucleation work? Relationship with vacuums?

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What is nucleation and how it works? In cosmology, which is the relationship that nucleation have with quantum tunneling, vacuums and Big Bang?
 

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hilbert2
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It's hard to tell what level of answer you expect, but I'd personally explain nucleation by using a diffusion analogy. If you drop a little bit of food coloring in a glass of water, it will start mixing with the water by diffusion and eventually there's about as much coloring in every small volume element of the liquid. Now, imagine that we're doing diffusion backwards in time (antidiffusion). Then if there's even a tiny bit more solute in one part of a liquid, the solute will start concentrating towards that point. But if you try to anti-diffuse a solution where there's exactly as much solute everwhere, the concentration profile doesn't change (and neither does it in forward-diffusion). So, here we have an example where a very small deviation from uniformity will "nucleate" the anti-diffusion process.
 
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What is nucleation and how it works? In cosmology, which is the relationship that nucleation have with quantum tunneling, vacuums and Big Bang?
We cannot answer questions out of the blue, since we do not write entire textbooks to answer a question. The more as
It's hard to tell what level of answer you expect
which makes it hard to answer at all. You should provide at least the level of your understanding and what you've found so far by Google or Wikipedia searches, or even better by looking for papers on the subject, e.g. on arxiv.org. This might be sources we don't really want to debate upon, but it could tell us where you stand and what in detail you didn't understand.

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