Hubble tensions: a historical statistical analysis

TL;DR

This paper analyzes historical measurements of the Hubble constant, revealing that underestimated errors may explain the apparent Hubble tension, and recalibrates the significance of this discrepancy.

Contribution

It provides a statistical recalibration of Hubble constant measurements, showing that the tension is less significant when accounting for underestimated errors.

Findings

Error bars are often underestimated in Hubble measurements.

The 4.4σ tension reduces to about 2.1σ after recalibration.

The most extreme claimed tensions could be statistical fluctuations.

Abstract

Statistical analyses of the measurements of the Hubble-Lema\^itre constant $H_0$ (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 $H_0$ 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 $x\sigma $ deviation is indeed equivalent in a normal distribution to $x_{\rm eq.}\sigma $s deviation in the frequency of values, where $x_{\rm eq.}=0.83x^{0.62}$. Hence, a 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 of frequencies, with an associated probability $P(>x_{\rm eq.})=0.036$ (1 in 28). This can be increased up to a equivalent tension of 2.5$\sigma $ in the worst of the cases of claimed 6$\sigma $ tension, which may anyway happen as a random statistical fluctuation.