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I have few question about the metastability of the vacuum.

First of all I am wondering if metastability of the vacuum mean metastability of the higgs potential, so that the higgs potential has a deeper minimum than that one at $v=246 GeV$ where it could tunnel to:

enter image description here (taken from https://physics.aps.org/articles/v8/108)

Then, if so, how is such a potential even possible in a renormalizable Lagrangian? It has to be at least of the order $\phi^6$ to be bound from below and have two minima right? In my knowledge a Lagrangian with a coupling constant of negative mass dimension is not renormalizable (at least not in 4 dimensions).

Further i would like to know why people think that our vacuum is metastable or even how to measure that. I have read that there a some cosmological approaches but this confuses me since then gravity is taken into account which is not even part of the Standard model.

So three question:

  • Vacuum metastable = Higgs potential meta stable (if not what else?)
  • If so, is there a $\phi^6$ term in the Lagrangian? -> renormalizable?
  • How to measure vacuum metastability?
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