Can Non-standard Recombination Resolve the Hubble Tension?

The inconsistent Hubble constant values derived from cosmic microwave background (CMB) observations and from local distance-ladder measurements may suggest new physics beyond the standard $\Lambda$CDM paradigm. It has been found in earlier works that, at least phenomenologically, non-standard recombination histories can reduce the $\gtrsim 4\sigma$ Hubble tension to $\sim 2\sigma$. Following this path, we vary physical and phenomenological parameters in RECFAST, the standard code to compute ionization history of the universe, to explore possible physics beyond standard recombination. We find that the CMB constraint on the Hubble constant is sensitive to the Hydrogen ionization energy and $2s \rightarrow 1s$ two-photon decay rate, both of which are atomic constants, and is insensitive to other details of recombination. Thus, the Hubble tension is very robust against perturbations of recombination history, unless exotic physics modifies the atomic constants during the recombination epoch.