Erratum: cosmological parameter estimation: impact of CMB aberration

Abstract

The peculiar motion of an observer with respect to the CMB rest frame induces an apparent deflection of the observed CMB photons, i.e. aberration, and a shift in their frequency, i.e. Doppler effect. Both effects distort the temperature multipoles aℓm's via a mixing matrix at any ℓ. The common lore when performing a CMB based cosmological parameter estimation is to consider that Doppler affects only the l = 1 multipole, and neglect any other corrections. In ref. [1] we checked the validity of this assumption in parameter estimation for a Planck-like angular resolution, both for a full-sky ideal experiment and also when sky cuts are included to model CMB foreground contaminations with a sky fraction similar to the Planck satellite. The result to this analysis was that aberration and Doppler have a sizable impact on a CMB based parameter estimation. In this erratum we correct an error made in ref. [1] when comparing pseudo angular power spectra computed in the CMB rest frame with the ones measured by a moving observer. Properly comparing the two spectra we find now that although the corrections to the Cℓ due to aberration and Doppler are larger than the cosmic variance at ℓ > 1000 and potentially important, the resulting bias on the parameters is negligible for Planck.