Model-independent constraints on reionization from large-scale cosmic microwave background polarization

On large angular scales, the polarization of the CMB contains information about the evolution of the average ionization during the epoch of reionization. Interpretation of the polarization spectrum usually requires the assumption of a fixed functional form for the evolution, e. g., instantaneous reionization. We develop a model-independent method where a small set of principal components completely encapsulates the effects of reionization on the large-angle E-mode polarization for any reionization history within an adjustable range in redshift. Using Markov chain Monte Carlo methods, we apply this approach to both the 3 year WMAP data and simulated future data. WMAP data constrain two principal components of the reionization history, approximately corresponding to the total optical depth and the difference between the contributions to the optical depth at high and low redshifts. The optical depth is consistent with the constraint found in previous analyses of WMAP data that assume instantaneous reionization, with only a slightly larger uncertainty due to the expanded set of models. Using the principal component approach, WMAP data also place a 95% confidence level upper limit of 0.08 on the contribution to the optical depth from redshifts z > 20. With improvements in polarization sensitivity and foreground modeling, approximately five of the principal components can ultimately be measured. Constraints on the principal components, which probe the entire reionization history, can test models of reionization, provide model-independent constraints on the optical depth, and detect signatures of high-redshift reionization.