Tachyonic Instability and Dynamics of Spontaneous Symmetry Breaking

TL;DR

This paper explores the rapid and efficient process of tachyonic preheating during spontaneous symmetry breaking, emphasizing how the potential's shape influences the dynamics and outcomes of the transition.

Contribution

It provides a detailed analysis of tachyonic preheating, highlighting the dependence of the process on the potential's shape near its maximum and describing different regimes of symmetry breaking.

Findings

Tachyonic preheating converts potential energy into scalar field waves within a single oscillation.

The process is solely due to tachyonic instability in models with quadratic potentials.

In models with higher-order potentials, tunneling, instability, and bubble collisions also play roles.

Abstract

Spontaneous symmetry breaking usually occurs due to the tachyonic (spinodal) instability of a scalar field near the top of its effective potential at $\phi = 0$. Naively, one might expect the field $\phi$ to fall from the top of the effective potential and then experience a long stage of oscillations with amplitude O(v) near the minimum of the effective potential at $\phi = v$ until it gives its energy to particles produced during these oscillations. However, it was recently found that the tachyonic instability rapidly converts most of the potential energy V(0) into the energy of colliding classical waves of the scalar field. This conversion, which was called "tachyonic preheating," is so efficient that symmetry breaking typically completes within a single oscillation of the field distribution as it rolls towards the minimum of its effective potential. In this paper we give a detailed description of tachyonic preheating and show that the dynamics of this process crucially depend on the shape of the effective potential near its maximum. In the simplest models where $V(\phi) \sim -m^2\phi^2$ near the maximum, the process occurs solely due to the tachyonic instability, whereas in the theories $-\lambda\phi^n$ with n > 2 one encounters a combination of the effects of tunneling, tachyonic instability and bubble wall collisions.