Hubble tensions: a historical statistical analysis

Abstract

ABSTRACT Statistical analyses of measurements of the Hubble–Lemaître constant H0 (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 per cent of the measurements. The fact that the underestimation of error bars for H0 is so common might explain the apparent discrepancy of values, which is formally known as the Hubble tension. Here we have carried out a recalibration of the probabilities with this sample of measurements. We find that thexσ deviation is indeed equivalent in a normal distribution to the xeqσ deviation in the frequency of values, where xeq = 0.83x0.62. Hence, a tension of 4.4σ, estimated between the local Cepheid–supernova distance ladder and cosmic microwave background (CMB) data, is indeed a 2.1σ tension in equivalent terms of a normal distribution of frequencies, with an associated probability P(>xeq) = 0.036 (1 in 28). This can be increased up to a equivalent tension of 2.5σ in the worst of the cases of claimed 6σ tension, which may occur anyway as a random statistical fluctuation.