Bubble formation in $\phi^6$ potential

TL;DR

This paper investigates bubble formation in a scalar field with a $\, ext{phi}^6$ potential, analyzing tunneling rates and the validity of approximations through numerical and analytical solutions at different temperatures.

Contribution

It provides new numerical solutions for bounce configurations and an analytical solution that covers both thin-wall and thick-wall regimes in $\, ext{phi}^6$ potential.

Findings

Numerical bounce solutions for symmetric configurations

Analytical bounce solution valid in thin-wall and thick-wall limits

Assessment of the thin-wall approximation's validity

Abstract

Scalar field theory with an asymmetric potential is studied at zero temperature and high-temperature for $\phi^6$ potential. The equations of motion are solved numerically to obtain O(4) spherical symmetric and O(3) cylindrical symmetric bounce solutions. These solutions control the rates for tunneling from the false vacuum to the true vacuum by bubble formation. The range of validity of the thin-wall approximation (TWA) is investigated. An analytical solution for the bounce is presented, which reproduces the action in the thin-wall as well as the thick-wall limits.