The effect of aberration on partial-sky measurements of the cosmic microwave background temperature power spectrum

TL;DR

This paper introduces an advanced harmonic-space method to accurately quantify how our motion-induced aberration affects partial-sky CMB measurements, revealing potential biases in cosmological parameter estimation.

Contribution

The authors develop a higher-order, efficient harmonic-space approach to model CMB aberration effects, improving accuracy over previous methods and accounting for window functions and pixelization.

Findings

Aberration causes a measurable shift in multipole moments (~0.1%).

Ignoring aberration biases the sound horizon measurement by ~0.01%.

Biases from aberration are significant for current CMB experiments.

Abstract

Our motion relative to the cosmic-microwave-background (CMB) rest frame deflects light rays giving rise to shifts as large as L -> L(1+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 L > 1/beta ~ 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 L/L ~ beta<cos(theta)>, with <cos(theta)> averaged over the survey footprint. Such a shift, if ignored, would bias the measurement of the sound-horizon size theta_* 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 cannot 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.