Large scale voids are a very prominent feature in recent redshift surveys: here we attempt an explanation in terms of a first order phase transition occurring during the slow roll epoch of a two field inflation. The ensuing bubble like perturbations -- nucleated at a number of e-folds Napprox 50 before reheating -- are thought to be the precursors of the voids we observe today. They pass the CMB constraints. Furthermore, the claim, in apparent conflict with inflation, that the Universe is open, may also be explained if we live in a superhorizon bubble nucleated around Napprox 60 and if the Universe itself be a collection of such bubbles. Our model predicts sharply peaked bubble spectra, e.g. at Omega0 ≅.2, so that our probability of living in the right bubble is close to one. Finally, one can even envision a sequence of two phase transitions, at N approx 60 and approx 50, where bubbles are born within bubbles. In conclusion, the study of the large scale structure may turn out to be a powerful probe -- maybe the only one -- of Planck physics.
