We show that the $H_0$ tension can be resolved by making recombination occur earlier, keeping the fit to cosmic microwave background (CMB) data almost intact. We provide a suite of general necessary conditions to give a good fit to CMB data while realizing a high value of $H_0$ suggested by local measurements. As a concrete example for a successful scenario with early recombination, we demonstrate that a model with a time-varying $m_e$ can indeed satisfy all of the conditions. We further show that such a model can also be well fitted to low-$z$ distance measurements of baryon acoustic oscillations (BAO) and type Ia supernovae (SNeIa) with a simple extension of the model. A time-varying $m_e$ in the framework of ${\mathrm{\Omega }}_k\mathrm{\Lambda }\mathrm{CDM}$ is found to be a sufficient and excellent example of a solution to the $H_0$ tension, yielding $H_0={72.3}_{-2.8}^{+2.7}\mathrm{km}/\sec /\mathrm{Mpc}$ from the combination of CMB, BAO, and SNeIa data even without incorporating any direct local $H_0$ measurements. Employing the Bayesian posterior predictive distribution, we find that this model can reduce the $H_0$ tension in the reference $\mathrm{\Lambda }\mathrm{CDM}$ model from $4.8\sigma$ down to $2.2\sigma$. Apart from the $H_0$ tension, this model is also favored from the viewpoint of the CMB lensing anomaly.

• Received 15 July 2020
• Revised 22 January 2021
• Accepted 17 March 2021

DOI:https://doi.org/10.1103/PhysRevD.103.083507