Finite Time Vacuum Survival Amplitude and Vacuum Energy Decay

TL;DR

This paper investigates vacuum energy decay by analyzing the vacuum survival amplitude over finite conformal time, considering both signs of the cosmological constant, and discusses decay behavior and transient effects at first order in coupling.

Contribution

It provides a finite time analysis of vacuum decay amplitudes in a cosmological setting, including transient effects and decay width estimation.

Findings

Late time decay behavior characterized for finite conformal time

Transient effects in vacuum survival amplitude analyzed

Decay width estimated at first order in coupling

Abstract

The problem of the vacuum energy decay is studied for both signs of the cosmological constant, through the analysis of the vacuum survival amplitude, defined in terms of the {\em conformal time}, $z$, by ${\mathcal A}(z,z^\prime)\equiv <\text{vac}\,z|\text{vac}\,z^\prime>$. Transition amplitudes are computed for finite time-span, $Z\equiv z^\prime-z$, and their {\em late time} behavior (directly related to the putative decay width of the state) as well as the transients are discussed up to first order in the coupling constant, $\lambda$.