Reconstructing the recombination history using cosmic microwave background and baryon acoustic oscillation data*

We present a data-driven reconstruction of the ionization history during the epoch of recombination, leveraging the constraining power of both cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) data sets. This constraining power arises mostly from the sensitivity of acoustic peak locations to the redshift of recombination, and the sensitivity of both the diffusion damping scale and small-scale polarization amplitude to the duration of recombination. Our approach avoids a commonly used linear response approximation, because it would lead to significantly biased results. The reconstructed ionization history is consistent with the standard recombination history, although parameter constraints are impacted due to the newly introduced degeneracies. We find that modifications to recombination can alleviate the Hubble tension to varying degrees depending on the datasets used. The 95% confidence upper limits on H0 are 73.0 (70.2) km/s/Mpc when CMB (CMB+BAO) data are included, assuming no other changes are made to the standard cosmological model. We forecast that adding forthcoming SPT-3G measurements to Planck and existing BAO data will shrink the constraints on the ionization history by about a factor of two.