Evidence for possible systematic underestimation of uncertainties in extragalactic distances and its cosmological implications

Abstract

We analyze 91,742 reported extragalactic distance moduli and their one sigma uncertainties for 14,560 galaxies with multiple reported distances in the NED Redshift-Independent Distances database. For every ordered pair of distance moduli measurements 1 and 2 for each galaxy, we define $\Delta (\sigma )_{1,2}$, a measure for how different measurement 2 is in relation to measurement 1, as a multiple of the reported one sigma uncertainty in measurement 1. For a given set of distance moduli measurements, we take a mean of all such $\Delta (\sigma )_{1,2}$ to determine the average separation between distance moduli of any galaxy in the set as a multiple of the reported uncertainty. For normally distributed measurements, the expected value of mean $\Delta (\sigma )$ is 0.79. Our results are as follows. The mean $\Delta (\sigma )$ of 1,239,062 ordered pairs of extragalactic distance moduli for 14,560 galaxies is 2.07 corresponding to a p-value of 3.85%. This indicates a possible systematic underestimation of uncertainties in extragalactic distances. We also find that the mean reported one sigma uncertainty decreased and the mean $\Delta (\sigma )$ increased from 1989 to 2018. This points to increased underestimation of uncertainties with time. For the latest period from 2014 to 2018 with 14,580 reported extragalactic distance moduli for 5,406 galaxies, the mean $\Delta (\sigma )$ of 40,462 ordered pairs is 3.00 corresponding to a p-value of 0.27%. For 14,888 extragalactic distance moduli of 2,518 galaxies measured using Type Ia Supernovae, the mean $\Delta (\sigma )$ for 124,016 ordered pairs is 2.85 corresponding to a p-value of 0.44%. These results may have some implications for our confidence in cosmological parameters and models. We conclude that more liberal estimation of uncertainties in future reported extragalactic distances should be considered. The results also give a possible way out of the Hubble-Lemaitre tension by advocating for increasing the error bars on Hubble-Lemaitre constant measured via distance ladders of standard candles and rulers.

Appendix

Table 3 Mean reported one sigma uncertainty and mean $\Delta(\sigma)$ for 44 distance measurement methods with multiple reported measurements for at least one galaxy in the NED database (Steer et al. 2017)

Table 4 Percentage of ordered pairs of extragalactic distance moduli over ranges of $\Delta(\sigma)$, for each of the 44 distance measurement methods with multiple reported measurements for at least one galaxy in the NED database (Steer et al. 2017)