Planck evidence for a closed Universe and a possible crisis for
  cosmology
  The recent Planck Legacy 2018 release has confirmed the presence of an
enhanced lensing amplitude in CMB power spectra compared to that predicted in
the standard $\Lambda$CDM model. A closed universe can provide a physical
explanation for this effect, with the Planck CMB spectra now preferring a
positive curvature at more than $99 \%$ C.L. Here we further investigate the
evidence for a closed universe from Planck, showing that positive curvature
naturally explains the anomalous lensing amplitude and demonstrating that it
also removes a well-known tension within the Planck data set concerning the
values of cosmological parameters derived at different angular scales. We show
that since the Planck power spectra prefer a closed universe, discordances
higher than generally estimated arise for most of the local cosmological
observables, including BAO. The assumption of a flat universe could, therefore,
mask a cosmological crisis where disparate observed properties of the Universe
appear to be mutually inconsistent. Future measurements are needed to clarify
whether the observed discordances are due to undetected systematics, or to new
physics, or simply are a statistical fluctuation.
