The evidence for a spatially flat Universe

Abstract

We use a new and statistically powerful Planck likelihood to show that the Planck temperature and polarization spectra are consistent with a spatially flat Universe, in contrast to recent claims in the literature. When combined with other astrophysical data, particularly geometrical measurements of baryon acoustic oscillations, our likelihood constrains the Universe to be spatially flat to extremely high precision. We deduce a curvature density parameter ωK = 0.0004 ± 0.0018 in good agreement with the 2018 results of the Planck team. In the context of inflationary cosmology, the observations offer strong support for models of inflation with a large number of e-foldings and disfavour models of incomplete inflation.