Closed universes from cosmological instantons

Current observational data are consistent with the universe being slightly closed. We investigate families of singular and nonsingular closed instantons that could describe the beginning of a closed inflationary universe. We calculate the scalar and tensor perturbations that would be generated from singular instantons and compute the corresponding CMB power spectrum in a universe with cosmological parameters like our own. We investigate spatially homogeneous modes of the instantons, finding unstable modes which render the instantons subdominant contributions in the path integral. We show that a suitable condition may be imposed on singular closed intantons, constraining their instabilities. With this constraint these instantons can provide a suitable model of the early universe, and predict CMB power spectra in close agreement with the predictions of slow-roll inflation.