Curvature tension: Evidence for a closed universe

Abstract

The curvature parameter tension between Planck 2018, cosmic microwave background (CMB) lensing, and baryon acoustic oscillation (BAO) data is measured using the suspiciousness statistic to be $2.5--3\ensuremath{\sigma}$. Conclusions regarding the spatial curvature of the Universe which stem from the combination of these data should therefore be viewed with suspicion. Without CMB lensing or BAO, Planck 2018 has a moderate preference for closed universes, with Bayesian betting odds of over $50\ensuremath{\mathbin:}1$ against a flat universe and over $2000\ensuremath{\mathbin:}1$ against an open universe.