We know we don't know

A few days ago on Nature Astronomy it was published a paper by a team of italian researchers with an unequivocal title: Planck evidence for closed Universe and a possible crisis for cosmology⁽⁶⁾. We can consider it as one of the first scientific articles that seriously takes into consideration a situation that it is becoming increasingly pressing: a crisis in cosmology.
The standard cosmological model, based on cosmic inflation⁽²⁾ and on empirical constants that evaluate unknown physical quantities as dark matter and dark energy, although very well verified, has not yet passed the last step: the detection of gravitational waves in cosmic microwave background (CMB). One of the fundamental points of this model, but also of many of the surviving competing models, is the accelerated expansion of spacetime at speed greater than that of light which explains the flatness of the early universe.
This flatness emerges in particular when studying the cosmic microwave background, the residual energy of the initial expansion of spacetime. This radiation has come down to us from the point where it was produced, a little less than 14 billion years ago, crossing the whole universe. This means that in the signal detected there must also be gravitational lens effects⁽¹⁾ due to the amount of matter, usual and dark, present in the universe. These effects have long been known and calculated⁽⁴⁾ and can already be seen in the image produced by Planck⁽⁵⁾.

Gravitational lensing of the Cosmic Microwave Background - via ESA

The italian team, after having examined the Planck data to test the gravitational lens effects, not only found that the distortions produced are higher than expected, but it was also pushed in stating that this discrepancy would be more easily explained by a closed universe model⁽⁶⁾, somthing like a sphere-shaped universe.
According to the authors this would introduce a crisis in cosmology⁽⁶⁾, a crisis that is already underway due to the discrepancy between the Hubble constant measured starting from the CMB and that measured using the observable universe.
The result, for now, is taken with due skepticism, as evident from the words of David Spergel of Princeton University:

It's a really important claim, but I'm not sure it's one that's backed by the data. In fact, I'd say the evidence is actually against it.

What I want to remember in this post is that the observable universe, including the one "photographed" by the CMB, is only a little portion of the whole universe, as easily deducible from the inflationary model, so an observable universe with flat geometry does not imply that the whole universe has a flat geometry, without forgetting that in mathematics there are many closed three-dimensional surfaces with flat geometry⁽³⁾.
So the only reasonable conclusion is that both our standard models, both cosmological and of elementary particles, need additional elements to provide a more precise understanding of the universe. Or maybe they should simply be rethought.

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1. The gravitational lens is a physical effect due to the presence of large masses between us and the light source capable of curving the path of photons in a way similar to what optical lenses do.
   Read also:
   Perlick, V. (2004). Gravitational lensing from a spacetime perspective. Living reviews in relativity, 7(1), 9. doi:10.12942/lrr-2004-9 ↩
2. A. H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D 23, 347 (1981). ↩
3. Conway, J. H., & Rossetti, J. P. (2003). Describing the platycosms. arXiv preprint arXiv:math/0311476 ↩
4. Lewis, A., & Challinor, A. (2006). Weak gravitational lensing of the CMB. Physics Reports, 429(1), 1-65. doi:10.1016/j.physrep.2006.03.002 (arXiv) ↩
5. Planck Collaboration (2018). Planck 2018 results. VIII. Gravitational lensing. arXiv preprint arXiv:1807.06210 ↩
6. Di Valentino, E., Melchiorri, A., & Silk, J. (2019). Planck evidence for a closed Universe and a possible crisis for cosmology. Nature Astronomy, 1-8. doi:10.1038/s41550-019-0906-9 (arXiv) ↩↩↩