Cosmology with a decaying vacuum

TL;DR

This paper investigates the quantum decay properties of false vacuum states in cosmology, revealing their long-term survival behavior and energy evolution towards the true vacuum over time.

Contribution

It provides a quantum theoretical analysis of false vacuum decay, highlighting non-exponential survival probabilities and energy convergence to the true vacuum at late times.

Findings

False vacuum states exhibit non-exponential decay at late times.

The survival probability follows an inverse power-law as time increases.

The energy of false vacuum states approaches that of the true vacuum as 1/t^2.

Abstract

Properties of unstable false vacuum states are analyzed from the point of view of the quantum theory of unstable states. Some of false vacuum states survive up to times when their survival probability has a non-exponential form. At times much latter than the transition time, when contributions to the survival probability of its exponential and non-exponential parts are comparable, the survival probability as a function of time t has an inverse power-like form. We show that at this time region the instantaneous energy of the false vacuum states tends to the energy of the true vacuum state as $1/t^{2}$ for $t \to \infty$.