Accurate cosmological parameter estimates using polarization data of the cosmic microwave background (CMB) put stringent requirements on map calibration, as highlighted in the recent results from the Planck satellite. In this paper, we point out that a model-dependent determination of polarization calibration can be achieved by the joint fit of the temperature-E-mode cross-power spectrum (TE) and E-mode auto-power spectrum (EE). This provides a valuable cross-check to band-averaged polarization efficiency measurements determined using other approaches. We demonstrate that, in $\mathrm{\Lambda }\mathrm{CDM}$, the combination of the TE and EE constrain polarization calibration with sub-percent uncertainty with Planck data and 2% uncertainty with sptpol data. We arrive at similar conclusions when extending $\mathrm{\Lambda }\mathrm{CDM}$ to include the amplitude of lensing $A_{\mathrm{L}}$, the number of relativistic species $N_{\mathrm{eff}}$, or the sum of the neutrino masses $\sum m_{\nu }$. The uncertainties on cosmological parameters are minimally impacted when marginalizing over polarization calibration, except, as can be expected, for the uncertainty on the amplitude of the primordial scalar power spectrum $\ln ({10}^{10}{A}_{\mathrm{s}})$, which increases by 20–50%. However, this information can be fully recovered by adding temperature auto-power spectrum (TT) information. For current and future ground-based experiments, SPT-3G and CMB-S4, we forecast the cosmological parameter uncertainties to be minimally degraded when marginalizing over polarization calibration parameters. In addition, CMB-S4 could constrain its polarization calibration at the level of $\sim 0.2\%$ by combining TE and EE, and reach $\sim 0.06\%$ by also including TT. We therefore conclude that relying on calibrating against Planck polarization maps, whose statistical uncertainty is limited to $\sim 0.5\%$, would be insufficient for upcoming experiments.

• Received 12 February 2021
• Accepted 15 June 2021

DOI:https://doi.org/10.1103/PhysRevD.104.023518