Decoupling redshift: The key to conciliate global and local estimates of the Universe expansion rate

To explain the $\sim4.4\sigma$ discrepancy between the local $74.03\pm1.42\ \text{kms}^{-1}\text{~Mpc}^{-1}$ and the global $67.4\pm0.5\ \text{kms}^{-1}\text{~Mpc}^{-1}$ estimates of the Universe expansion rate, H0, becomes one of the most challenging problems in contemporary cosmology. Underestimated systematic errors as well as new physics beyond the standard ΛCDM model, has been invoked to solve, or at least alleviate, this problem. In this paper we show that we can conciliate the local measurement of the Hubble constant with its global estimate in a very simple way without making any of these assumptions. This is achieved if we deal with the decoupling redshift, $z_*$ , as a free parameter. By noting that the dependence of the cosmic microwave background (CMB) observables on H0 comes from the decoupling redshift $z_*$ we show that, by incorporating a missing parameter, the electron fraction $X_e(z_*)$ , to the $z_*$ functional form, local and global estimates of H0 agree with each other perfectly. The effect of introducing $X_e(z_*)$ is the same that treat $z_*$ as free parameter which should be fitted along with the model parameters. The CMB data and the local estimates of H0 are reconciled if $z_*\approx1163$ , a value $\sim6.5\%$ higher than the value obtained from the usual calculations