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, {\it i.e.} aberration, and a shift in their frequency, {\it i.e.} Doppler effect. Both effects distort the temperature multipoles $a_{\ell m}$'s via a mixing matrix at {\it any} $\ell$. 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 check 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. Assuming a simple fiducial cosmological model with five parameters, we simulated CMB temperature maps of the sky 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. Although the correction on the power spectrum ${C_\ell}$ is larger than the cosmic variance at $\ell>1000$ and potentially important, we find that the bias on the parameters is negligible for Planck.