Tensions in cosmological parameters measurement motivate a revisit of the effects of instrumental systematics. In this article, we focus on the Pearsons correlation coefficient of the cosmic microwave background temperature and polarization E modes $mathcal{R}_ell^{rm TE}$ which has the property of not being biased by multiplicative instrumental systematics. We build a $mathcal{R}_ell^{rm TE}$-based likelihood for the Planck data, and present the first constraints on $Lambda$CDM parameters from the correlation coefficient. Our results are compatible with parameters derived from a power spectra based likelihood. In particular the value of the Hubble parameter $H_0$ characterizing the expansion of the Universe today, 67.5 $pm$ 1.3 km/s/Mpc, is consistent with the ones inferred from standard CMB analysis. We also discuss the consistency of the Planck correlation coefficient with the one computed from the most recent ACTPol power spectra.
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