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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 cosmic microwave background power spectra compared with that predicted in the standard Λ cold dark matter model, where Λ is the cosmological constant. A closed Universe can provide a physical explanation for this effect, with the Planck cosmic microwave background spectra now preferring a positive curvature at more than the 99% confidence level. 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 in the Planck dataset 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 baryon acoustic oscillations. 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.

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Fig. 1: Preference for a closed Universe, ΩK < 0, from Planck.
Fig. 2: Degeneracy between curvature and lensing.
Fig. 3: Curvature and shift in parameters.
Fig. 4: Tension with BAO.
Fig. 5: Tension with CMB lensing.
Fig. 6: Tension with cosmic shear measurements.
Fig. 7: Tension with combined data.
Fig. 8: Tensions in combined data.

Data availability

The data that support the plots within this paper and other findings of this study are available at or from the corresponding author upon reasonable request.

Code availability

All of the codes used to produce the presented results are publicly available. See Methods for more details.


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E.D.V. acknowledges support from the European Research Council in the form of a Consolidator Grant with number 681431. A.M. thanks the University of Manchester and the Jodrell Bank Centre for Astrophysics for hospitality. A.M. is supported by TAsP, iniziativa specifica INFN. We thank M. Melchiorri for discussions.

Author information




E.D.V. performed all MCMC analyses, simulations and the Planck parameters analysis at different scales, produced all the figures, wrote the paper and helped with additional ideas. A.M. proposed the main idea, performed the tension analyses and wrote the paper. J.S. wrote the paper and helped with additional ideas.

Corresponding author

Correspondence to Alessandro Melchiorri.

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Di Valentino, E., Melchiorri, A. & Silk, J. Planck evidence for a closed Universe and a possible crisis for cosmology. Nat Astron 4, 196–203 (2020).

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