Assessing the robustness of sound horizon-free determinations of the Hubble constant
Tristan L. Smith, Vivian Poulin, Théo Simon
Abstract
The Hubble tension can be addressed by modifying the sound horizon (${r}_{s}$) before recombination, triggering interest in early universe estimates of the Hubble constant, ${H}_{0}$, independent of ${r}_{s}$. Constraints on ${H}_{0}$ from an ${r}_{s}$-free analysis of the full shape BOSS galaxy power spectra within $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ were recently reported and used to comment on the viability of physics beyond $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. Here we demonstrate that ${r}_{s}$-free analyses with current data depend on both the model and the priors placed on the cosmological parameters, such that $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ analyses cannot be used as evidence for or against new physics. We find that beyond-$\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ models which introduce additional energy density with significant pressure support, such as early dark energy (EDE) or additional neutrino energy density ($\mathrm{\ensuremath{\Delta}}{N}_{\mathrm{eff}}$), lead to ${r}_{s}$-free values of ${H}_{0}$ which are larger by $3--4\text{ }\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$. On the other hand, models which only affect the time of recombination, such as a varying electron mass ($\mathrm{\ensuremath{\Delta}}{m}_{e}$), produce ${H}_{0}$ constraints similar to $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. Using BOSS data, constraints from light element abundances, cosmic microwave background (CMB) lensing, a CMB-based prior on the primordial scalar amplitude (${A}_{s}$), spectral index (${n}_{s}$), and ${\mathrm{\ensuremath{\Omega}}}_{m}$ from the $\mathrm{Pantheon}+\text{Type}$ Ia supernovae dataset, we find that in $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, ${H}_{0}=64.9\ifmmode\pm\else\textpm\fi{}2.2\text{ }\text{ }\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$; in EDE, ${H}_{0}={68.7}_{\ensuremath{-}3.9}^{+3}$; in $\mathrm{\ensuremath{\Delta}}{N}_{\mathrm{eff}}$, ${H}_{0}={68.1}_{\ensuremath{-}3.8}^{+2.7}$; and in $\mathrm{\ensuremath{\Delta}}{m}_{e}$, ${H}_{0}={64.7}_{\ensuremath{-}2.3}^{+1.9}$. Using a prior on the angular size of the sound horizon at baryon drag from BAO and CMB measurements, these values become in $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, ${H}_{0}=67.9\ifmmode\pm\else\textpm\fi{}1.7$; in EDE, ${H}_{0}={72.2}_{\ensuremath{-}3.8}^{+2.9}$; in $\mathrm{\ensuremath{\Delta}}{N}_{\mathrm{eff}}$, ${H}_{0}={71.5}_{\ensuremath{-}3.3}^{+2.5}$; and in $\mathrm{\ensuremath{\Delta}}{m}_{e}$, ${H}_{0}=68.0\ifmmode\pm\else\textpm\fi{}1.7$. With current data, none of the models are in significant tension with $\mathrm{S}{H}_{0}\mathrm{ES}$, and consistency tests based on comparing ${H}_{0}$ posteriors with and without ${r}_{s}$ marginalization are inconclusive with respect to the viability of beyond $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ models.