We try to find conditions, the fulfillment of which allows a universe born in
a metastable false vacuum state to survive and not to collapse. The conditions
found are in the form of inequalities linking the depending on time $t$
instantaneous decay rate ${\it\Gamma}(t)$ of the false vacuum state and the
Hubble parameter $H(t)$. Properties of the decay rate of a quantum metastable
states are discussed and then the possible solutions of the conditions found
are analyzed and discussed. Within the model considered it is shown that a
universe born in the metastable vacuum state has a very high chance of
surviving until very late times if the lifetime, $\tau_{0}^{F}$, of the
metastable false vacuum state is much shorter, than the duration of the
inflation process. Our analysis shows that the instability of the electroweak
vacuum does not have to result in the tragic fate of our Universe leading to
its death.
