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 x _e (z) 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, ${\hat{C}}_{\ell }^{\text{TE}}$ , has roughly one quarter of the constraining power of ${\hat{C}}_{\ell }^{\text{EE}}$ on the reionization optical depth τ, and its addition improves the precision on τ by 20% over using ${\hat{C}}_{\ell }^{\text{EE}}$ only. We also use a two-step reionization model with an additional high-redshift step, parameterized by an early ionization fraction $x_e^{\text{min}}$ , and a late reionization step at z _re. We find that future high signal-to-noise measurements of the multipoles 10 ⩽ ℓ < 20 are especially important for breaking the degeneracy between $x_e^{\text{min}}$ and z _re. In addition, we show that the uncertainties on these parameters determined from a map with sensitivity 10 microK 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.