Bubbles without cores

Abstract

The decay of a false vacuum in a theory without a true vacuum is studied. Using variational arguments, we find that for a class of potentials of the type a${\ensuremath{\varphi}}^{i}$+b${\ensuremath{\varphi}}^{j}$ (a>0,b<0 and i<j) the necessary condition for the existence of bounce solutions in four dimensions is 2\ensuremath{\le}i<j<4. The thin-wall condition breaks down for these solutions, but not necessarily for the semiclassical approximation. A bounce solution associated with potential ${m}^{2}$${\ensuremath{\varphi}}^{2}$-\ensuremath{\eta}${\ensuremath{\varphi}}^{3}$+\ensuremath{\lambda}${\ensuremath{\varphi}}^{4}$ is presented to discuss the transition from a thin-wall bubble to a thick-walled one. The validity conditions of using these solutions to describe the false vacuum decay within the framework of the semiclassical approximation are discussed.