Predictions of the Thomson scattering optical depth. The gray line and region represent the measurement provided by Planck, i.e., τ_e = 0.0544 ± 0.0073. The red solid, blue dashed, and green dotted–dashed lines correspond to the results shown in Figure 3. The red shaded region represents the values of ﹩24.15\lt \langle \mathrm{log}{f}_{{\rm{esc}}}{\xi }_{{\rm{ion}}}\rangle \lt 24.54﹩ constrained by the measured errors.