Closed Universes from Cosmological Instantons

Current observational data is consistent with the universe being slightly closed. We investigate families of singular and non-singular 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 sub-dominant contributions in the path integral. We show that a suitable condition may be imposed on singular closed instantons, 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.