Footprints of Doppler and Aberration Effects in CMB Experiments: Statistical and Cosmological Implications

In the frame of the Solar System, the Doppler and aberration effects cause distortions in the form of mode couplings in the cosmic microwave background (CMB) temperature and polarization power spectra and hence impose biases on the statistics derived by the moving observer. We explore several aspects of such biases and pay close attention to their effects on CMB polarization which previously have not been examined in detail. A potentially important bias that we introduce here is $\textit{boost variance}$---an additional term in cosmic variance, induced by the observer's motion. Although this additional term is negligible for whole-sky experiments, in partial-sky experiments it can reach $10\%$ (temperature) to $20\%$ (polarization) of the standard cosmic variance ($\sigma$). Furthermore, we investigate the significance of motion-induced $\textit{power}$ and $\textit{parity}$ asymmetries in TT, EE, and TE as well as potential biases induced in cosmological parameter estimation performed with whole-sky TTTEEE. Using Planck-like simulations, we find that our local motion induces $\sim1-2 \%$ hemispherical asymmetry in a wide range of angular scales in the CMB temperature and polarization power spectra; however, it does not imply any significant amount of parity asymmetry or shift in cosmological parameters. Finally, we examine the prospects of measuring the velocity of the Solar System w.r.t. the CMB with future experiments via the mode coupling induced by the Doppler and aberration effects. Using the CMB TT, EE, and TE power spectra up to $\ell=4000$, SO and CMB-S4 can make a dipole-independent measurement of our local velocity respectively at $8.5\sigma$ and $20\sigma$.