Dzień dobry, [cc cosmo-media mailing list]
Napiszę po angielsku, ale możemy zmienić między językami jak będzie potrzebny.
Apparently you are interested in the article Cyr-Racine et al 2022:
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.201301.
The article presents a rather speculative, but interesting, hypothesis about mirror matter, offering a possible explanation of the Hubble constant puzzle.
The article starts with a mathematical rescaling aimed at understanding the relation between the standard cosmological and observations, and proposes that this purely mathematical exercise could have a physical interpretation in terms of mirror matter.
The first paragraph on page 201301-3 gives a brief description of "mirror matter", and how (if it exists) it would relate to ordinary matter.
Figure 1 shows that the authors' mirror matter model would be consistent with the statistics of Planck observations of the cosmic microwave background.
Figure 2 shows that the model could provide a high value of the Hubble constant, of about 73 km/s/Mpc, and what the values of other parameters would have to be for the model to be observationally viable.
* Figure 2 bottom-left and bottom-right show values of parameters of the model that are most likely not observable.
* Figure 2 top-right shows the value of the helium abundance Y_p that would be required, and the text (left-hand column of page 201301-4) gives the numbers involved. The helium abundance is well-constrained observationally, and the text acknowledges that a bit more speculation regarding properties of the model is needed in order for the model to become observationally viable - this is discussed more on page 201301-4. In other words, the model does not quite work, and the authors suggest future calculations that might help.
Personally, I find a more likely explanation of the Hubble constant puzzle to be much simpler, related to the fact that the Universe is inhomogeneous. In terms of real observations, the local part of the Universe that we observe is necessarily smaller than more distant parts of the Universe; as a first approximation, this is a simple geometric effect. Deviations from the average are generally higher in smaller spatial regions. Our observations (made within our lifetime) necessarily come from light that passes through our local Universe - which is not quite the same as an "average" part of the Universe. So deviations on small scales are not so surprising. The difficulty is doing the modelling correctly, which is an ongoing research task.
You could look at these some of the following articles by our cosmology group for more details of this class of explanations for dark energy and for the Hubble constant puzzle, although this work is still research in progress:
* https://ui.adsabs.harvard.edu/abs/2013JCAP...10..043R * https://ui.adsabs.harvard.edu/abs/2013IJMPD..2241018R * https://ui.adsabs.harvard.edu/abs/2015CQGra..32u5021B * https://ui.adsabs.harvard.edu/abs/2016IJMPD..2530007B
Cheers Boud