Inference of gravitational lensing and patchy reionization with future CMB data

We develop an optimal Bayesian solution for jointly inferring secondary signals in the cosmic microwave background (CMB) originating from gravitational lensing and patchy screening during epoch of reionization. This method is able to extract full information content data, improving upon previously considered quadratic estimators screening. forecast constraints using marginal unbiased score expansion method, show that they are largely dominated by CMB polarization, depend on exact details For models consistent with current data which produce largest signals, a detection ($3\text{ }\ensuremath{\sigma}$) cross-correlation between possible SPT-3G autocorrelation CMB-S4. Models lowest evade sensitivity but still detect CMB-S4 via their cross-correlation.