Metric perturbations from quantum tunneling in open inflation

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Abstract
We study the effect that quantum fluctuations produced during the nucleation of a single-bubble open inflationary universe have on the amplitude of temperature anisotropies in the cosmic microwave background. We compute the instanton action for the quantum tunneling between the false and true vacua in open inflation models and relate the amplitude of quantum fluctuations in the bubble wall to primordial curvature perturbations. We show that quantum fluctuations of the bubble wall are sensitive to the gravitational effects of the true vacuum and find the parameters of open inflation models for which their contribution to the temperature anisotropy in the microwave background can be neglected. We also study the contribution from long wavelength super-curvature modes and constrain the parameters of the models so that they do not distort the observed anisotropy