Cosmological “constant” in a universe born in the metastable false vacuum state

Abstract

AbstractThe cosmological constant $$\varLambda $$ Λ 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 $$\varLambda = \varLambda (t)$$ Λ = Λ ( 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 $$E(t) \simeq E_{min} + \alpha _{2}/t^{2}+\ldots $$ E ( t ) ≃ E min + α 2 / t 2 + … in the late last phase of the decay process. (Here $$E_{min}$$ 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 $$\varLambda $$ Λ can have a very great value resulting from the quantum field theory calculations in the early universe in the inflationary era, $$\varLambda \simeq \varLambda _{qft}$$ Λ ≃ Λ qft , and then it can later be quickly reduced to the very, very small values.