Interpreting the CMB aberration and Doppler measurements: boost or
  intrinsic dipole?
  The aberration and Doppler coupling effects of the Cosmic Microwave
Background (CMB) were recently measured by the Planck satellite. The most
straightforward interpretation leads to a direct detection of our peculiar
velocity $\beta$, consistent with the measurement of the well-known dipole. In
this paper we discuss the assumptions behind such interpretation. We show that
Doppler-like couplings appear from two effects: our peculiar velocity and a
second order large-scale effect due to the dipolar part of the gravitational
potential. We find that the two effects are exactly degenerate but only if we
assume second-order initial conditions from single-field Inflation. Thus,
detecting a discrepancy in the value of $\beta$ from the dipole and the Doppler
couplings implies the presence of a primordial non-Gaussianity. We also show
that aberration-like signals likewise arise from two independent effects: our
peculiar velocity and lensing due to a first order large-scale dipolar
gravitational potential, independently on Gaussianity of the initial
conditions. In general such effects are not degenerate and so a discrepancy
between the measured $\beta$ from the dipole and aberration could be accounted
for by a dipolar gravitational potential. Only through a fine-tuning of the
radial profile of the potential it is possible to have a complete degeneracy
with a boost effect. Finally we discuss that we also expect other signatures
due to integrated second order terms, which may be further used to disentangle
this scenario from a simple boost.
