Planck Internal Closed-Universe Preference (Ω_K < 0)

The Planck 2018 temperature power spectra, analyzed alone, prefer a spatially closed universe: the curvature parameter comes out at -0.095 < Omega_K < -0.007 at 99 percent confidence, with closure favored at more than 99 percent (Di Valentino, Melchiorri and Silk 2020, Nature Astronomy; arXiv:1911.02087). The preference is driven by the same feature as the lensing-amplitude anomaly: the observed acoustic peaks are smoothed as if gravitational lensing were roughly 10 to 20 percent stronger than the best-fit flat model predicts, and a small positive curvature absorbs the excess naturally. Taken at face value this breaks the inflationary expectation of flatness and undermines the internal consistency of the standard model fit.

ΛCDM cannot keep both its datasets and its geometry. When BAO measurements are combined with Planck the closed preference disappears and Omega_K returns to zero, but Handley (2019) and Di Valentino et al. showed that Planck and BAO disagree at more than 3 sigma once curvature is allowed, so the combination that restores flatness mixes datasets that are mutually inconsistent in the curved model, a statistically questionable move. The model therefore faces a trilemma: accept closure and break BAO concordance, force flatness and carry an unexplained lensing excess, or attribute the signal to an unidentified systematic. Within ΛCDM the lensing information in the peak smoothing must come entirely from the catalogued matter distribution in a flat FLRW background, so the model has nowhere to put the excess except into the geometry itself.

The standing of the anomaly has softened but not closed. The reanalyzed Planck PR4/NPIPE maps reduce the lensing excess (CamSpec gives A_lens = 1.095 +/- 0.056, HiLLiPoP 1.039 +/- 0.052) and with it the curvature pull, and ACT DR6 measures A_lens = 1.007 +/- 0.057, consistent with flatness. Whether the original signal was a real physical effect, a statistical fluctuation, or a residual systematic in the PR3 likelihoods remains debated; what is agreed is that the closed-universe episode exposed how sensitively the inferred geometry of the universe depends on a small unmodeled lensing-like smoothing in the CMB acoustic peaks.

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