Our motion relative to the cosmic-microwave-background ( CMB ) rest frame deflects light rays giving rise to shifts as large as \ell \to \ell ( 1 \pm \beta ) , where \beta = 0.00123 is our velocity ( in units of the speed of light ) on measurements CMB fluctuations .
Here we present a novel harmonic-space approach to this CMB aberration that improves upon prior work by allowing us to ( i ) go to higher orders in \beta , thus extending the validity of the analysis to measurements at \ell \gtrsim \beta ^ { -1 } \simeq 800 ; and ( ii ) treat the effects of window functions and pixelization in a more accurate and computationally efficient manner .
We calculate precisely the magnitude of the systematic bias in the power spectrum inferred from the partial sky , and show that aberration shifts the multipole moment by \Delta \ell / \ell \simeq \beta \left < \cos \theta \right > , with \left < \cos \theta \right > averaged over the survey footprint .
Such a shift , if ignored , would bias the measurement of the sound-horizon size \theta _ { \mathrm { * } } at the 0.01 \% -level , which is comparable to the measurement uncertainties of Planck .
The bias can then propagate into cosmological parameters such as the angular-diameter distance , Hubble parameter and dark-energy equation of state .
We study the effect of aberration for current Planck , South Pole Telescope ( SPT ) and Atacama Cosmology Telescope ( ACT ) data and show that the bias can not be neglected .
We suggest that the small tension between Planck , ACT , and SPT may be due partially to aberration .
An Appendix shows how the near constancy of the full-sky power spectrum under aberration follows from unitarity of the aberration kernel .