Beyond Optical Depth: Future Determination of Ionization History from the Cosmic Microwave Background.

We explore the fundamental limits to which reionization histories can be constrained using only large-scale cosmic microwave background (CMB) anisotropy measurements. The redshift distribution of the fractional ionization () affects the angular distribution of CMB polarization. We project constraints on the reionization history of the universe using low-noise full-sky temperature and E-mode measurements of the CMB. We show that the measured TE power spectrum, , has roughly one quarter of the constraining power of on the reionization optical depth , and its addition improves the precision on by 20% over using only. We also use a two-step reionization model with an additional high-redshift step, parameterized by an early ionization fraction , and a late reionization step at . We find that future high signal-to-noise measurements of the multipoles 10 ⩽ < 20 are especially important for breaking the degeneracy between and . In addition, we show that the uncertainties on these parameters determined from a map with sensitivity 10 K arcmin are less than 5% larger than the uncertainties in the noiseless case, making this noise level a natural target for future large sky area E-mode measurements.