  The current central experimental values of the parameters of the Standard
Model give rise to a striking conclusion: metastability of the electroweak
vacuum is favoured over absolute stability. A metastable vacuum for the Higgs
boson implies that it is possible, and in fact inevitable, that a vacuum decay
takes place with catastrophic consequences for the Universe. The metastability
of the Higgs vacuum is especially significant for cosmology, because there are
many mechanisms that could have triggered the decay of the electroweak vacuum
in the early Universe. We present a comprehensive review of the implications
from Higgs vacuum metastability for cosmology along with a pedagogical
discussion of the related theoretical topics, including renormalization group
improvement, quantum field theory in curved spacetime and vacuum decay in field
theory.

Cosmology and Nongalactic Astrophysics;High Energy Physics - Phenomenology;High Energy Physics - Theory