The second statement suggests in a fixed coordinate any chosen bubble would be the largest in its own cluster, but this is a coordinate-dependent statement, after choosing the bubble, one can always find another coordinate in which there are bigger bubbles in the same cluster. According to these statements, if the nucleation rate of bubbles is small, we will end up with bubbles that form clusters and will not collide with each other, with the heat release from vacuum decay stored in the domain-walls, quite different from what the hot Big-Bang starts from. This problem called "graceful exit problem", discussed independently later by Hawking, Moss and Stewart, then solved by the proposal of new inflation by Linde, Abrecht and Steinhardt, which makes use of Coleman-Weinberg mechanism to generate the inflation potential that satisfies slow-roll conditions. Lee–Weinberg–Yi metric The existence of magnetic monopoles has long been an interesting and profound possibility. Such solitons could potentially explain the quantization of electric charge, as pointed out by Dirac; they can arise as the classical solutions in gauge theories, as pointed out by Polyakov and 't Hooft; and the inability to detect them is one of the motivations of proposing a period of inflation before the hot Big-Bang phase. The dynamics of magnetic monopole solutions is especially simple when the theory is at BPS limit---when it can be extended to include fermionic sectors to form a supersymmetric theory. In these cases, the multi-monopole solutions can be explicitly obtained, the monopoles in a system are basically free because the interaction mediated by Higgs field is cancelled by the gauge interaction. in the case of a maximally broken gauge group into , the multi-monopole solution can be viewed as weakly interacting particles, each carrying a phase factor, therefore when considering the low energy processes the total number of degrees of freedom for n monopoles is 4n, in 4-dimensional spacetime---3 for spatial position and one for the phase factor. The dynamics can be reduced to the motion inside a 4n dimensional space with a nontrivial metric from the interactions among the monopoles, so called "moduli space approximation". Erick Weinberg, with Kimyeong Lee and Piljin Yi, did a calculation for the moduli space metric in the case of well-separated monopoles, with an arbitrary large compact gauge group maximally broken into products of U(1)'s, and argued that in some certain cases the metric can be exact---valid for crowded monopole