Evidence for Possible Systematic Underestimation of Uncertainties in Extragalactic Distances and Its Cosmological Implications

Abstract

We analyse 91,742 reported extragalactic distance moduli and their uncertainties for all 14,560 galaxies with multiple reported distances in the NED Redshift-Independent Distances database. For each ordered pair of distance moduli measurements 1 and 2 for each galaxy, we define Δ(σ)[1, 2], a measure for how different measurement 2 is in relation to measurement 1, as a multiple of the estimated standard deviation in measurement 1. We then take a mean of all such Δ(σ)[1, 2] in a given category to come up with an estimate for the average separation between measurements as a multiple of the average reported uncertainty in that category. For normally distributed measurements, the expected value of Δ(σ) is 1.13. Our results are as follows. The mean Δ(σ) of all 1,239,062 ordered pairs of extragalactic distance moduli 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 one sigma reported uncertainty decreased and the mean Δ(σ) increased from 1991-2018. This points to increased underestimation of uncertainties with time. For the latest period 2011-2018 with 26,509 reported extragalactic distance moduli for 7,812 galaxies, the mean Δ(σ) of 124,840 ordered pairs is 2.72 corresponding to a p-value of 0.65%. For 14,888 extragalactic distance moduli of 2,518 galaxies measured using Type Ia Supernovae, the mean Δ(σ) for 124,016 ordered pairs is 2.85 corresponding to a p-value of 0.44%. This 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 tension by advocating for increasing the error bars on Hubble-Lemaitre constant measured via distance ladders of standard candles and rulers.