Tachyonic instability and dynamics of spontaneous symmetry breaking

Abstract

Spontaneous symmetry breaking usually occurs due to the tachyonic (spinodal) instability of a scalar field near the top of its effective potential at $\ensuremath{\varphi}=0.$ Naively, one might expect the field $\ensuremath{\varphi}$ 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 $\ensuremath{\varphi}=v$ 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 [G. Felder et al., Phys. Rev. Lett. 87, 011601 (2001)]. In this paper we give a detailed description of tachyonic preheating and show that the dynamics of this process crucially depends on the shape of the effective potential near its maximum. In the simplest models where $V(\ensuremath{\varphi})\ensuremath{\sim}\ensuremath{-}{m}^{2}{\ensuremath{\varphi}}^{2}/2$ near the maximum, the process occurs solely due to the tachyonic instability, whereas in the theories $\ensuremath{-}\ensuremath{\lambda}{\ensuremath{\varphi}}^{n}$ with $n>2$ one encounters a combination of the effects of tunneling, tachyonic instability and bubble wall collisions.