IS THERE A BIG-BUBBLE PROBLEM IN EXTENDED INFLATION

We present a generalization of the thin-wall formalism to calculate the evolution of true-vacuum bubbles in "extended" inflation. For inflaton quartic couplings of the order M/M(PI), gravity will lead to the recollapse of bubbles during most of the extended-inflation period thereby altering the bubble size distribution. The completion of the phase transition will proceed through tiny bubbles satisfying homogeneity constraints of the microwave background for arbitrary values of omega. Thus, it is possible to construct models that agree with experiments even for the original version of extended inflation.