Multiverse as an ensemble of stable and unstable Universes

Estimates of the Higgs and top quark masses, $m_{H} \simeq 125.10 \pm 0.14$ [GeV] and $m_{t} \simeq 172.76 \pm 0.30$ [GeV] based on the experimental results place the Standard Model in the region of the metastable vacuum. A consequence of the metastability of the Higgs vacuum is that it should induce the decay of the electroweak vacuum in the early Universe with catastrophic consequences. It may happen that certain universes were lucky enough to survive the time of canonical decay, that is the exponential decay, and live longer. This means that it is reasonable to analyze conditions allowing for that. We analyze properties of an ensemble of Universes with unstable vacua considered as an ensemble of unstable systems from the point of view of the quantum theory of unstable states. We found some symmetry relations for quantities characterizing the metastable state. We also found a relation linking the decay rate, ${\it\Gamma}$ of the metastable vacuum state with the Hubble parameter $H(t)$, which may help to explain why a universe with an unstable vacuum that lives longer then the canonical decay times need not decay.

K. Urbanowski · 2015