New Semiclassical Picture of Vacuum Decay

We introduce a new picture of vacuum decay which, in contrast to existing semiclassical techniques, provides a real-time description and does not rely on classically forbidden tunneling paths. Using lattice simulations, we observe vacuum decay via bubble formation by generating realizations of vacuum fluctuations and evolving with the classical equations of motion. The decay rate obtained from an ensemble of simulations is in excellent agreement with existing techniques. Future applications include bubble correlation functions, fast decay rates, and decay of nonvacuum states.

Figure 1

A classically allowed false vacuum decay for the Lagrangian density Eq. (3) with $\lambda =1.2$ and ${\varphi }_0=(\pi /4\sqrt{2})$. The initial fluctuations $\delta \varphi$ and $\delta \dot{\varphi }$ are realizations of Gaussian random fields with spectra mimicking Minkowski false vacuum fluctuations. We observe the dynamical emergence of a bubble with field localized near a true vacuum ($\cos \varphi =1$) embedded within the false vacuum ($\cos \varphi =-1$). This explicitly demonstrates the existence of classically allowed paths for false vacuum decay.

Figure 2

Decay rates of false vacuum initial states as ${\varphi }_0$ is varied for our ensembles of lattice simulations (orange dots). For comparison, the blue solid line is the analytic prediction Eq. (9) with $g=-1+{\lambda }^2=0.44$ to set the overall scale to the false vacuum mass, and the gray dashed line is the leading-order prediction (i.e., $\mathrm{\Gamma }=A{e}^{-2\pi C(\lambda ){\varphi }_0^2}$ with the constant $A$ normalized so the curves match at ${\varphi }_0=1$). We fixed $\lambda =1.2$ and $(V_0/{\varphi }_0^2{\mu }^2)=8\times {10}^{-3}$.