Planck evidence for a closed Universe and a possible crisis for cosmology

Abstract

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 $Λ$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.

Figures (8)

• Figure 1: Preference for a closed universe, $\Omega_k<0$, from Planck. Posterior distributions on the curvature density parameter $\Omega_K$ from Planck 2018 (PL18) temperature and polarization-simulated angular power spectra (assuming a fiducial flat $\Lambda$CDM model) and PL18 real data adopting the baseline Planck likelihood and the alternative CAMSPEC likelihood, respectively. For comparison, the posterior from the previous Planck 2015 planck2015 (PL15) data release is also shown.
• Figure 2: Degeneracy between curvature and lensing. Constraints at $68 \%$ and $95 \%$ in the $A_{lens}$ vs $\Omega_K$ plane from Planck 2018 temperature and polarization data. A degeneracy between curvature and the $A_{lens}$ parameter is clearly present. Note that a model with $\Omega_K<0$ is slightly preferred with respect to a flat model with $A_{lens}>1$.
• Figure 3: Curvature and parameters shift. Cosmological parameters derived from two different multipoles ranges ($2\le\ell\le800$ and $800<\ell\le2500$) of the Planck 2018 temperature and polarization data assuming either a $\Lambda$CDM model (Left) or a closed model (Right). Polarization data at low multipoles ($2\le \ell \le 30$) is included in both cases. The difference in the parameter constraints present in flat $\Lambda$CDM, disappears when assuming a model with $\Omega_k=-0.045$.
• Figure 4: Tension with BAO. Acoustic-scale distance measurements divided by the corresponding mean distance ratio from PL18 temperature and polarization power spectra in a $\Lambda$CDM$+\Omega_K$ model. The green bands show the $68\%$ and $95\%$ confidence ranges. The data points correspond to the measurements at $68\%$ C.L. from the following experiments: 6dFGS 6dFGS, SDSS MGS mgs, and BOSS DR12 bossdr12 (the BAO dataset considered in this paper). We also report measurements from WiggleZ wigglez, DES des, DR14 LRG lrg, SDSS quasars sdssqso, and BOSS Lyman-$\alpha$bosslya.
• Figure 5: Tension with CMB lensing. The solid lines are the theoretical predictions for the best-fits CMB lensing power spectra from the PL18 angular spectra in case of $\Lambda$CDM, $\Lambda$CDM+$\Omega_K$, and $\Lambda$CDM+$A_{lens}$ models, respectively. The $\Lambda$CDM+$\Omega_K$ model has $\Omega_K=-0.0438$ while the flat $\Lambda$CDM+$A_{lens}$ model has $A_{lens}=1.191$. The gray bands are the CMB lensing conservative experimental band powers extracted from the Planck 2018 trispectrum data.