Cosmological "constant" in a universe born in the metastable false
  vacuum state
  The cosmological constant $\Lambda$ is a measure of the energy density of the
vacuum. Therefore properties of the energy of the system in the metastable
vacuum state reflect properties of $\Lambda = \Lambda(t)$. We analyze
properties of the energy, $E(t)$, of a general quantum system in the metastable
state in various phases of the decay process: In the exponential phase, in the
transition phase between the exponential decay and the later phase, where decay
law as a function of time $t$ is in the form of powers of $1/t$, and also in
this last phase. We found that this energy having an approximate value
resulting from the Weisskopf--Wigner theory in the exponential decay phase is
reduced very fast in the transition phase to its asymptotic value $E(t) \simeq
E_{min} + \alpha_{2}/t^{2}+\ldots$ in the late last phase of the decay process.
(Here $E_{min}$ is the minimal energy of the system). This quantum mechanism
reduces the energy of the system in the unstable state by a dozen or even
several dozen orders or more. We show that if to assume that a universe was
born in metastable false vacuum state then according to this quantum mechanism
the cosmological constant $\Lambda$ can have a very great value resulting from
the quantum field theory calculations in the early universe in the inflationary
era, $\Lambda \simeq \Lambda_{qft}$, and then it can later be quickly reduced
to the very, very small values.
