Absolute Lower Bound on the Bounce Action

Understand

The decay rate of a false vacuum is determined by the minimal action solution of the tunnelling field: bounce.

• In this Letter, we focus on models with scalar fields which have a canonical kinetic term in $N(>2)$ dimensional Euclidean space, and derive an absolute lower bound on the bounce action.
• In the case of four-dimensional space, we show the bounce action is generically larger than $24/\lambda_{\rm cr}$, where $\lambda_{\rm cr} \equiv {\rm max} [ -4V(\phi) /|\phi|^4] $ with the false vacuum being at $\phi=0$ and $V(0)=0$.
• We derive this bound on the bounce action \textit{without solving the equation of motion explicitly}.