Can redshift errors bias measurements of the Hubble Constant?

Abstract

Redshifts have been so easy to measure for so long that we tend to neglect the fact that they too have uncertainties and are susceptible to systematic error. As we strive to measure cosmological parameters to better than 1% it is worth reviewing the accuracy of our redshift measurements. Surprisingly small systematic redshift errors, as low as 10 −4 , can have a significant impact on the cosmological parameters we infer, such as H 0 . Here we investigate an extensive (but not exhaustive) list of ways in which redshift estimation can go systematically astray. We review common theoretical errors, such as adding redshifts instead of multiplying by (1 + z); using v = cz; and using only cosmological redshift in the estimates of luminosity and angular-diameter distances. We consider potential observational errors, such as rest wavelength precision, air to vacuum conversion, and spectrograph wavelength calibration. Finally, we explore physical effects, such as peculiar velocity corrections, galaxy internal velocities, gravitational redshifts, and overcorrecting within a bulk flow. We conclude that it would be quite easy for small systematic redshift errors to have infiltrated our data and be impacting our cosmological results. While it is unlikely that these errors are large enough to resolve the current H 0 tension, it remains possible, and redshift accuracy may become a limiting factor in near future experiments. With the enormous efforts going into calibrating the vertical axis of our plots (standard candles, rulers, clocks, and sirens) we argue that it is now worth paying a little more attention to the horizontal axis (redshifts).

Resolving the Hubble tension with new early dark energy

“…For example, in Ref. [14], it was found that redshift uncertainties cannot account for the discrepancy, and, in Refs. [15][16][17], a similar conclusion was drawn with regard to the local Hubble flow.…”

Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory

“…Explanations for the tension between direct measurements and CMB estimates range from underestimated systematic errors or modeling of the primordial power spectrum (e.g., Davis et al 2019;Dhawan et al 2020;Anderson 2019;Hazra et al 2019), to models for dark energy (e.g., Li & Shafieloo 2019;Alestas et al 2020;Di Valentino et al 2020), to unmodeled pre-recombination physics that lead to a decreased sound horizon scale (e.g., Poulin et al 2019;Chiang & Slosar 2018;Beradze & Gogberashvili 2020;Vagnozzi 2019;Lin et al 2019;Arendse et al 2019). See Knox & Millea (2020) for a review of possible solutions to the tension.…”

The Tension over the Hubble-Lemaitre Constant

“…The expansion factors a, strictly proportional to the recession velocities, are calculated from a = 1/(1 + z) = ν/ν 0 and are not modified, since observational errors of redshift determinations are tiny compared to errors about D L . Though this has been recently contested if the reader carefully examines the data they will agree with our assessment of relative error [37].…”

“…Both measures are used for historical reasons, magnitude being related to luminosity as perceived by the human eye being approximately the log(luminosity). Some astronomers actually worry more about relatively minor redshift errors than investigate the larger distance errors [37]. Third, results and parameters from this type of analysis (pseudo-H-routine) are interesting and immediately useful in today's astrophysics.…”