Implicit inference of the reionization history with higher-order statistics of the 21-cm signal

The Epoch of Reionization (EoR), when the first luminous sources ionised the intergalactic medium, represents a new frontier in cosmology. The Square Kilometre Array Observatory (SKAO) will offer unprecedented insights into this era through observations of the redshifted 21-cm signal, enabling constraints on the Universe’s reionization history. We investigate the information content of the average neutral hydrogen fraction ($\bar{x}_{\rm HI}$) in several Gaussian (spherical and cylindrical power spectra) and non-Gaussian (Betti numbers and bispectrum) summary statistics of the 21-cm signal. Mock 21-cm observations are generated using the AA* configuration of SKAO’s low-frequency telescope, incorporating noise levels for 100 and 1000 hours. We employ a state-of-the-art implicit inference framework to learn posterior distributions of $\bar{x}_{\rm HI}$ in redshift bins centred at z = 8.0, 7.2 and 6.5, for each statistic and noise scenario, validating the posteriors through calibration tests. Using the figure of merit to assess constraining power, we find that Betti numbers alone are on average more informative than the power spectra, while the bispectrum provides limited constraints. However, combining higher-order statistics with the cylindrical power spectrum improves the mean figure of merit by ~0.25 dex (~33 % reduction in $\sigma (\bar{x}_{\rm HI})$). The relative contribution of each statistic varies with the stage of reionization. With SKAO observations approaching, our results show that combining power spectra with higher-order statistics can significantly increase the information retrieved from the EoR, maximising the scientific return of future 21-cm observations.