We calculate analytically the bubble nucleation rate in a model of first
order inflation which is able to produce large scale structure. The computation
includes the first-order departure from the thin-wall limit, the explicit
derivation of the pre-exponential factor, and the gravitational correction. The
resulting bubble spectrum is then compared with constraints from the large
scale structure and the microwave background. We show that there are models
which pass all the constraints and produce bubble-like perturbations of
interesting size. Furthermore, we show that it is in principle possible to
reconstruct completely the inflationary two-field potential from observations.Comment: Accepted for publication in Phys. Rev. D, 19 pages, 2 ps figs
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