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There is a big-bubble problem in extended inflation.

We expand on the observation by Weinberg that in extended inflation the present value of the Planck mass is determined not dynamically but instead by the parameters of the inflation potential. For the simplest choices of potential, extended inflationary universes are inconsistent with the thin-wall approximation for bubble nucleation. Even where the thin-wall approximation applies, the proposed resolution of the big-bubble problem by Goldwirth and Zaglauer cannot be realized in a working scenario