Stability of Q-Balls and Catastrophe

Abstract

We propose a practical method for analyzing stability of Q-balls for the whole parameter space, which includes the intermediate region between the thin-wall limit and thick-wall limit as well as Q-bubbles (Q-balls in false vacuum), using catastrophe theory. We apply our method to the two concrete models, V3 = m2φ2/2 − µφ3 + λφ4 and V4 = m2φ2/2 − λφ4 + φ6/M2. We find that V3 and V4 Models fall into fold catastrophe and cusp catastrophe, respectively, and their stability structures are quite different from each other.