Abstract
We show that by jointly fitting cosmic microwave background (CMB) and astrophysical data---a compilation of UV luminosity data from the Hubble Frontier Field and neutral hydrogen data from distant source---we can infer on the shape of the evolution of the ionized hydrogen fraction with redshift, in addition to constraining the average optical depth $\ensuremath{\tau}$. For this purpose, we introduce here a novel extended model that includes hydrogen ionization histories which are monotonic with redshift, but allow for an asymmetry, as indicated from our previous works on a free-form reconstruction of reionization. By using our baseline data combination, we obtain $\ensuremath{\tau}=0.054{2}_{\ensuremath{-}0.0028}^{+0.0017}$, consistent with our previous works and tighter than the one inferred by Planck 2018 data because of the combination of CMB with astrophysical data. We find that the symmetric hypothesis within our parametrization is disfavored at $4\ensuremath{\sigma}$. We test our findings by using alternative likelihoods for CMB polarization at low multipoles, i.e. based on the 2020 reprocessing of Planck high frequency instrument data or on the joint analysis of Wilkinson microwave anisotropy probe and Planck low frequency instrument data, obtaining consistent results that disfavor the symmetric hypothesis of the reionization history at a high statistically significant level. These results will be further tested by more precise astrophysical data such as that from JWST and Euclid deep fields.