Higgs mechanism and vacuum instability

[lark]

Does the shape of the Higgs potential change if the energy of the vacuum changes?
According to Wikipedia,
If a more stable vacuum state were able to arise, then existing particles and forces would no longer arise as they presently do. Different particles or forces would arise from (and be shaped by) whatever new quantum states arose. The world we know depends upon these particles and forces, so if this happened, everything around us, from subatomic particles to galaxies, and all fundamental forces, would be reconstituted into new fundamental particles and forces and structures.

Is this right?
If so, it sounds like if the universe transitioned to a more stable vacuum state, then there might no longer be a Higgs mechanism, because all the particles including the Higgs particle, would change?
How would the shape of the Higgs potential change, if the energy of the vacuum were only very slightly lower? i.e. if you do a infinitesimal perturbation, lowering the energy of the vacuum?
Again, I am NOT asking whether the vacuum is currently metastable.

 

[mfb]

There would be no Higgs mechanism in the way we know it, yes.

The shape of the Higgs potential doesn't change from such a transition, we would just be at a different point in this potential.

How would the shape of the Higgs potential change, if the energy of the vacuum were only very slightly lower? i.e. if you do a infinitesimal perturbation, lowering the energy of the vacuum?

No that doesn't work. We are in a local minimum, a small perturbation does nothing (unless you count "producing a Higgs boson" as a small perturbation, in that case: It makes scientists happy).