Tachyonic instability and dynamics of spontaneous symmetry breaking

Spontaneous symmetry breaking usually occurs due to the tachyonic (spinodal) instability of a scalar field near the top of its effective potential at $\phi =0.\mathrm{}$ 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 $O\left(v\right)\mathrm{}$ 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 $V\left(0\right)\mathrm{}$ 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 $V\left(\phi \right)\sim -m^2{\phi }^2/2\mathrm{}$ near the maximum, the process occurs solely due to the tachyonic instability, whereas in the theories $-\lambda {\phi }^n$ with $n>\mathrm{}2\mathrm{}$ one encounters a combination of the effects of tunneling, tachyonic instability and bubble wall collisions.