A tale of two (or more) h's

Abstract

Abstract We use the large-scale structure galaxy data (LSS) from the BOSS and eBOSS surveys, in combination with abundances information from Big Bang Nucleosynthesis (BBN), to measure two values of the Hubble expansion rate, H 0 = 100h [ km s-1 Mpc-1], each of them based on very different physical processes. One is a (traditional) late-time-background measurement, based on determining the BAO scale and using BBN abundances on baryons for calibrating its absolute size (BAO+BBN). This method anchors H 0 to the (standard) physics of the sound horizon scale at pre-recombination times. The other is a newer, early-time based measurement, associated with the broadband shape of the power spectrum. This second method anchors  H 0 to the physics of the matter-radiation equality scale, which also needs BBN information for determining the suppression of baryons in the power spectrum shape (shape+BBN). Within the ΛCDM model, we find very good consistency among these two H 0's: BAO+BBN (+growth) delivers H 0 = 67.42+0.88 -0.94 (67.37+0.86 -0.95) km s-1Mpc-1, whereas the shape+BBN (+growth) delivers H 0 = 70.1+2.1 -2.1 (70.1+1.9 -2.1) km s-1  Mpc-1, where `growth' stands for information from the late-time-perturbations captured by the growth of structure parameter. These are the tightest sound-horizon free H 0 constraints from LSS data to date. As a consequence, to be viable any ΛCDM extension proposed to address the so-called “Hubble tension” needs to modify consistently not only the sound horizon scale physics, but also the matter-radiation equality scale, in such a way that both late- and early-based H 0's return results mutually consistent and consistent with the high H 0 value recovered by the standard cosmic distance ladder (distance-redshift relation) determinations.