Spectrum of cosmological perturbations in the one-bubble open universe

The spectrum of cosmological perturbations in the context of the one-bubble open inflation model is discussed, taking into account fluctuations of the metric. We find that, quite generically,thin wall single field models have no supercurvature modes. However, single field models with supercurvature modes do exist. In these models the density parameter Omega becomes a rando m variable taking a range of values inside of each bubble. We also show tha t the model dependence of the continuous spectrum for both scalar and tense r-type perturbations is small as long as the kinetic energy density of the background field does not dominate the total energy density. We conclude th at the spectrum of the density perturbation predicted in the single-field m odel of the one-bubble open inflation is rather robust. We also consider th e spectrum of scalar and tensor perturbations in a model of the Hawking-Tur ok type, without a false vacuum. (C) 1999 Elsevier Science B.V. All rights reserved.