Open inflation with an arbitrary false vacuum mass

We calculate the power spectrum of adiabatic density perturbations in an open inflationary model in which inflation occurs in two stages. First an epoch of old inflation creates a large, smooth universe, solving the horizon and homogeneity problems. Then an open universe emerges through the nucleation of a single bubble, with constant density hypersurfaces inside the bubble having constant negative spatial curvature. An epoch of ‘‘slow roll’’ inflation, shortened to give ${\mathrm{\Omega }}_0$<1 today, occurs within the bubble, which contains our entire observable universe. In this paper we compute the resulting density perturbations in the same ‘‘new thin wall’’ approximation used in a previous paper, but for an arbitrary positive mass of the inflaton field in the false vacuum satisfying ${\mathit{m}}^2$/${\mathit{H}}^2$≥2 where H is the Hubble constant during old inflation.