The great question about the Hubble constant

The Hubble-Lemaitre law is the mathematical formula bout the expanding universe. One of the collateral results of Einstein's theory of relativity was an expanding and non-static universe, a result that, in a first time, Einstein himself had disavowed. Yet various observations made in the second half of the 20s of the twentieth century instead confirmed the hypothesis of cosmic expansion^{(1, 2)}. \[z = H_0 \frac{D}{c}\] where $c$ is the speed of light, $H_0$ is the Hubble constant, while $z$ and $D$ are the light's redshift and the distance of the galaxy from the observer. The redshift, in particular, is due to the Doppler effect applied to electromagnetic waves. For example, when you hear the siren of an ambulance, it will seem to you stronger or weaker if approaching or moving away from your position. An electromagnetic wave, like light, instead will be closer to blue or red depending on whether it is closer to or away from the observer.
So, it has a certain importance to measure the redshift of the galaxies around us: evidently a null or little redshift was a clue to a static universe, otherwise we live in a dynamic universe, as you can see from the image present in the historical Hubble article⁽²⁾:

In order to measure the Hubble constant we use two different strategies: measuring the curvature of a cosmic triangle in the cosmic backgorund radiation or using the signal from the cepheid variable stars. In the first case we have a value of $67.4 \, (km/s) / Mpc$, where $Mpc$ is megaparsec, and from cepheid stars we have $74 \, (km/s) / Mpc$, so we can see that there is a little problem with one of the most important constant of the universe.
In a paper that will be published on Astrophysical Journal, Wendy Freedman et al. performed a new precise measure that is indipendent from Cepheid stars. Using the red giant stars they found a value that is compatible with cmb: $69.8 \pm 0.8 \pm 1.7 \, (km/s) / Mpc$. Despite this result, Freedman says:

The Hubble constant is the cosmological parameter that sets the absolute scale, size and age of the universe; it is one of the most direct ways we have of quantifying how the universe evolves. The discrepancy that we saw before has not gone away, but this new evidence suggests that the jury is still out on whether there is an immediate and compelling reason to believe that there is something fundamentally flawed in our current model of the universe.

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1. Lemaître, G., Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques (1927); english version (1931) ↩
2. Hubble, E. (1929). A relation between distance and radial velocity among extra-galactic nebulae. Proceedings of the National Academy of Sciences, 15 (3), 168-173 doi:10.1073/pnas.15.3.168 (scan) ↩↩