Towards a 1% Measurement of the Hubble Constant: Accounting for Time Dilation in Variable Star Light Curves

Abstract

Assessing the significance and implications of the recently established Hubble tension requires the comprehensive identification, quantification, and mitigation of uncertainties and/or biases affecting $H_0$ measurements. Here, we investigate the previously overlooked distance scale bias resulting from the interplay between redshift and Leavitt laws in an expanding Universe: Redshift-Leavitt bias (RLB). Redshift dilates oscillation periods of pulsating stars residing in supernova-host galaxies relative to periods of identical stars residing in nearby (anchor) galaxies. Multiplying dilated $\log{P}$ with Leavitt Law slopes leads to underestimated absolute magnitudes, overestimated distance moduli, and a systematic error on $H_0$. Emulating the SH0ES distance ladder, we estimate an associated $H_0$ bias of $(0.27 \pm 0.01)$% and obtain a corrected $H_0 = (73.70 \pm 1.40) \rm{km s^{-1} Mpc^{-1}}$. RLB becomes increasingly relevant as distance ladder calibrations pursue greater numbers of ever more distant galaxies hosting both Cepheids (or Miras) and type-Ia supernovae. The measured periods of oscillating stars can readily be corrected for heliocentric redshift (e.g. of their host galaxies) in order to ensure $H_0$ measurements free of RLB.