Hubble constant and sound horizon from the late-time Universe
Xue Zhang, Qing-Guo Huang
Abstract
We measure the expansion rate of the recent Universe and the calibration scale of the baryon acoustic oscillation (BAO) from low-redshift data. BAO relies on the calibration scale, i.e., the sound horizon at the end of drag epoch ${r}_{d}$, which often imposes a prior of the cosmic microwave background (CMB) measurement from the Planck satellite. In order to make really independent measurements of ${H}_{0}$, we leave ${r}_{d}$ completely free and use the BAO data sets combined with the 31 observational $H(z)$ data, GW170817, and Pantheon sample of Type Ia supernovae. In lambda cold dark matter ($\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$) model, we get ${H}_{0}=68.6{3}_{\ensuremath{-}1.77}^{+1.75}\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, ${r}_{d}=146.8{5}_{\ensuremath{-}3.77}^{+3.29}\text{ }\text{ }\mathrm{Mpc}$. For the two model-independent reconstructions of $H(z)$, we obtain ${H}_{0}=68.02\ifmmode\pm\else\textpm\fi{}1.82\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, ${r}_{d}=148.1{8}_{\ensuremath{-}3.78}^{+3.36}\text{ }\text{ }\mathrm{Mpc}$ in the cubic expansion, and ${H}_{0}=68.58\ifmmode\pm\else\textpm\fi{}1.76\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, ${r}_{d}=148.0{2}_{\ensuremath{-}3.60}^{+3.63}\text{ }\text{ }\mathrm{Mpc}$ in the polynomial expansion. The values of Hubble constant ${H}_{0}$ and sound horizon ${r}_{d}$ are consistent with the estimate derived from the Planck CMB data assuming a flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, but ${H}_{0}$ is in $2.4\ensuremath{\sim}2.6$ $\ensuremath{\sigma}$ tension with SH0ES 2019, respectively.