The sound of an object moving away from you will shift to a lower frequency as the waves from your point of view are spread out. This is the Doppler effect and applies to light waves as well. Edwin Hubble noticed that the light from distant galaxies was red shifted, that is, the wavelength of the light we received from them was longer, implying in a similar way that the galaxies were moving away and that the further ones were moving away faster. This was taken to mean that all the galaxies were moving away from a common centre as if there had been a Big Bang 13.6 billion years in the past. There are other ways to view it as well in QI, but let's stick with this image for simplicity for now.
Looking at local galaxies, the Hubble expansion rate has been measured to be 73 km/s/Mpc. That is, galaxies one megaparsec (Mpc) away from us are apparently moving away from us at 73 km/s. Recently, a new method was devised to predict the Hubble constant from observations of the Cosmic Microwave Background, that represents the cosmos at a redshift of Z=1000, and then extrapolate forward using standard models assuming dark matter and dark energy. Perhaps not surprisingly they predicted a slower cosmos: 67.7 km/s/Mpc. The difference between these values is now beyond a plausible level of chance, so it is a real problem (See Ref).
Now let us calculate what part of this predicted Hubble constant they would miss given that they do not include the extra acceleration due to quantised inertia. It would be 2x10-10 m/s2 over the lifetime of the universe (4.4x1017s) at the cosmic edge (radius = 4.4x1026m). OK. So what would it be at only 1Mpc distance (1Mpc = 3x1022m)?
dH = 2x10^-10 x 3x10^22 x 4.4x10^17 / 4.4x10^26 = 6 km/s/Mpc
The observed discrepancy in the Hubble constant is 5.3 km/s/Mpc. Nice!
For headaches and Hubble tension, just take QI!
Riess, A. et al., 2019. Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛCDM. The Astrophysical Journal, Volume 876, Issue 1, article id. 85, 13 pp.