Hubble tensions: a historical statistical analysis

Abstract

Statistical analyses of the measurements of the Hubble-Lemaître constant 0 (163 measurements between 1976 and 2019) show that the statistical error bars associated with the observed parameter measurements have been underestimated-or the systematic errors were not properly taken into account-in at least 15-20% of the measurements. The fact that the underestimation of error bars for 0 is so common might explain the apparent discrepancy of values, which is formally known today as the Hubble tension.Here we have carried out a recalibration of the probabilities with this sample of measurements. We find that deviation is indeed equivalent in a normal distribution to eq. s deviation in the frequency of values, where eq. = 0.83 0.62 . Hence, a tension of 4.4 , estimated between the local Cepheid-supernova distance ladder and cosmic microwave background (CMB) data, is indeed a 2.1 tension in equivalent terms of a normal distribution of frequencies, with an associated probability (> eq. ) = 0.036 (1 in 28). This can be increased up to a equivalent tension of 2.5 in the worst of the cases of claimed 6 tension, which may anyway happen as a random statistical fluctuation.