Underestimation of Hubble constant error bars: a historical analysis

Abstract

An analysis of a historical compilation of Hubble-Lema\^itre constant values ($H_0$: 163 data points measured between 1976 and 2019) assuming the standard cosmological model gives a $\chi^2$ value of the dispersion with respect to the weighted average of 580, much larger than the number of points, which has an associated probability that is very low. This means that Hubble tensions were always present in the literature, due either to the underestimation of statistical error bars associated with the observed parameter measurements, or to the fact that systematic errors were not properly taken into account in many of the measurements. The fact that the underestimation of error bars for $H_0$ is so common might explain the apparent 4.4-sigma discrepancy by Riess et al. As a matter of fact, more recent precise $H_0$ measurements with JWST data by Freedman et al. using standard candles in galaxies find there is no tension with CMBR data, possibly indicating that previously Riess et al. had underestimated their errors. Here we have carried out a recalibration of the probabilities. The tension of 4.4-$\sigma $, estimated between the local Cepheid-supernova distance ladder and cosmic microwave background (CMB) data, is indeed a 2.1-$\sigma $ tension in equivalent terms of a normal distribution, with an associated probability $P$ = 0.036 (1 in 28). This can be increased to an equivalent tension of 2.5-$\sigma $ in the worst cases of claimed 6-$\sigma $ tension, which may in any case happen as a random statistical fluctuation. If Hubble tensions were always present in the literature, and present day tensions are not more important than previous ones, why, then, is there so much noise and commotion surrounding Hubble tension after 2019? It is suggested here that this obeys a sociological phenomenon of ``groupthink''.