Cosmology with the cosmic microwave background temperature-polarization correlation

We demonstrate that the cosmic microwave background (CMB) temperature-polarization cross-correlation provides accurate and robust constraints on cosmological parameters. We compare them with the results from temperature or polarization and investigate the impact of foregrounds, cosmic variance, and instrumental noise. This analysis makes use of the Planck high-` HiLLiPOP likelihood based on angular power spectra, which takes into account systematics from the instrument and foreground residuals directly modelled using Planck measurements. The temperature-polarization correlation (TE) spectrum is less contaminated by astrophysical emissions than the temperature power spectrum (TT), allowing constraints that are less sensitive to foreground uncertainties to be derived. For Lambda CDM parameters, TE gives very competitive results compared to TT. For basic Lambda CDM model extensions (such as A(L), Sigma(mv) , or N-eff), it is still limited by the instrumental noise level in the polarization maps.