Periodic Bounce for Nucleation Rate at Finite Temperature in Minisuperspace Models

TL;DR

This paper explicitly derives periodic bounce configurations for quantum tunneling in minisuperspace cosmological models at finite energy, showing their properties and phase transition behavior.

Contribution

It extends the understanding of bounce solutions to finite energy cases in minisuperspace models, highlighting their monotonic period increase and phase transition characteristics.

Findings

Bounce period increases with energy monotonically

No bifurcations in periodic bounce solutions

First order phase transition confirmed

Abstract

The periodic bounce configurations responsible for quantum tunneling are obtained explicitly and are extended to the finite energy case for minisuperspace models of the Universe. As a common feature of the tunneling models at finite energy considered here we observe that the period of the bounce increases with energy monotonically. The periodic bounces do not have bifurcations and make no contribution to the nucleation rate except the one with zero energy. The sharp first order phase transition from quantum tunneling to thermal activation is verified with the general criterions.