We study the impact of the large-angle CMB polarization datasets publicly released by the WMAP and Planck satellites on the estimation of cosmological parameters of the \Lambda CDM model .
To complement large-angle polarization , we consider the high resolution ( or ‘ ‘ high- \ell ’ ’ ) CMB datasets from either WMAP or Planck as well as CMB lensing as traced by Planck ’ s measured four point correlation function .
In the case of WMAP , we compute the large-angle polarization likelihood starting over from low resolution frequency maps and their covariance matrices , and perform our own foreground mitigation technique , which includes as a possible alternative Planck 353 GHz data to trace polarized dust .
We find that the latter choice induces a downward shift in the optical depth \tau , roughly of order 2 \sigma , robust to the choice of the complementary high resolution dataset .
When the Planck 353 GHz is consistently used to minimize polarized dust emission , WMAP and Planck 70 GHz large-angle polarization data are in remarkable agreement : by combining them we find \tau = 0.066 ^ { +0.012 } _ { -0.013 } , again very stable against the particular choice for high- \ell data .
We find that the amplitude of primordial fluctuations A _ { s } , notoriously degenerate with \tau , is the parameter second most affected by the assumptions on polarized dust removal , but the other parameters are also affected , typically between 0.5 and 1 \sigma .
In particular , cleaning dust with Planck ’ s 353 GHz data imposes a 1 \sigma downward shift in the value of the Hubble constant H _ { 0 } , significantly contributing to the tension reported between CMB based and direct measurements of the present expansion rate .
On the other hand , we find that the appearance of the so-called low \ell anomaly , a well-known tension between the high- and low-resolution CMB anisotropy amplitude , is not significantly affected by the details of large-angle polarization , or by the particular high- \ell dataset employed .