Numerical simulation of the false vacuum decay at finite temperature

Abstract

The false vacuum decay rate is of important meaning in understanding the Universe, such as the symmetry breaking process in the early universe and the age of our universe, which is conventionally calculated with the saddle-point approximation in the field theory. Utilizing the extension of the Wigner function in quantum field theory, we numerically calculate the decay rate of the false vacuum through path integral. We study the decay rate for the thermal fluctuation scenarios and its dependence on the potential shape, and found that the false vacuum decay occurs following an exponentially decay rate, and the speed of vacuum decay decreases when the initial energy of the system decreases and the potential height increase. The discrepancy between the simulation results and the theoretical prediction of finite temperature effective field theory is observed.

Figures (11)

• Figure 1: A schematic illustration of the solution of $W[\phi, \Pi ;t]$, which describes the evolution of the system's state via the classical equations of motion.
• Figure 2: The $V$–$\phi$ diagram. $\phi_m$ denotes the field value at the potential maximum; $V_b$ is the barrier height; $\Delta V$ is the potential energy difference between the two vacua; FV and R indicate the false vaccum and the true vacuum repectively.
• Figure 3: The ratio of the initial energy density $\rho_E$ to the barrier height $\bar{V}_b$ as a function of $\beta$ for different values of $V_b$. The vertical dashed lines indicate the corresponding $\beta_c \omega^{\star}$ for each $V_b$.
• Figure 4: The decay rate as a function of temperature for different barrier heights. Simulation results are shown as points, solid lines represent the fitting curves, and dash-dotted lines indicate the instanton predictions. Vertical dashed lines correspond to different values of $\beta_c \omega^{\star}$. Lines with the same color represent the same potential.
• Figure 5: Left: Statistical distribution of initial field values at different temperatures, where the four vertical dashed lines indicate the field values $\phi_m/f^{\star}$ at the barriers of the four potentials in the right panel. Right: The four potentials under study with different barrier heights.