Cosmological parameter estimation: impact of CMB aberration

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 a_lm'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 this paper we reconsider the validity of this assumption, showing that it is actually not robust when sky cuts are included to model CMB foreground contaminations. Assuming a simple fiducial cosmological model with five parameters, we simulated CMB temperature maps of the sky in a WMAP-like and in a Planck-like experiment and added aberration and Doppler effects to the maps. We then analyzed with a MCMC in a Bayesian framework the maps with and without aberration and Doppler effects in order to assess the ability of reconstructing the parameters of the fiducial model. We find that, depending on the specific realization of the simulated data, the parameters can be biased up to one standard deviation for WMAP and almost two standard deviations for Planck. Therefore we conclude that in general it is not a solid assumption to neglect aberration in a CMB based cosmological parameter estimation.