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.
