Cosmological "constant" in a universe born in the metastable false vacuum state

Understand

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.