Asymmetric Symmetry Breaking: Unequal Probabilities of Vacuum Selection

TL;DR

This paper introduces a model where symmetry breaking leads to unequal probabilities of vacuum states, influenced by the potential's curvature, providing a potential explanation for cosmic asymmetries.

Contribution

The work presents a novel mechanism for asymmetric vacuum selection based on stochastic analysis of scalar fields with non-smooth potentials.

Findings

Probability depends on the square root of the second derivative of the potential.

Theoretical derivation using Fokker-Planck equations matches numerical simulations.

Potential implications for understanding cosmic asymmetries.

Abstract

Spontaneous symmetry breaking is a fundamental notion in modern physics, ranging from high energy to condensed matter. However, the usual spontaneous symmetry breaking only considers the equal probability to select the vacua. In this work, we conceive a model to realize the unequal probability of the symmetry breaking, leading to an unbalanced number of ground states. Specifically, we study the probabilities of a scalar field to roll down from the top of a potential, where the top is only $C^1$ continuous. As the whole system is subject to random perturbations, we find that the probability for the field to roll down to the left or right side depends the square root of the second derivative of the potential at the top. We solve this problem theoretically by using the Fokker-Planck equations in stochastic process and verify our findings numerically. This study may potentially be a new mechanism to explain the origins of asymmetries in the Universe.