Real Space Approach to CMB deboosting

The effect of our Galaxy's motion through the Cosmic Microwave Background rest frame, which aberrates and Doppler shifts incoming photons measured by current CMB experiments, has been shown to produce mode-mixing in the multipole space temperature coefficients. However, multipole space determinations are subject to many difficulties, and a real-space analysis can provide a straightforward alternative. In this work we describe a numerical method for removing Lorentz- boost effects from real-space temperature maps. We show that to deboost a map so that one can accurately extract the temperature power spectrum requires calculating the boost kernel at a finer pixelization than one might naively expect. In idealized cases that allow for easy comparison to analytic results, we have confirmed that there is indeed mode mixing among the spherical harmonic coefficients of the temperature. We find that using a boost kernel calculated at Nside=8192 leads to a 1% bias in the binned boosted power spectrum at l~2000, while individual Cls exhibit ~5% fluctuations around the binned average. However, this bias is dominated by pixelization effects and not the aberration and Doppler shift of CMB photons that causes the fluctuations. Performing analysis on maps with galactic cuts does not induce any additional error in the boosted, binned power spectra over the full sky analysis. For multipoles that are free of resolution effects, there is no detectable deviation between the binned boosted and unboosted spectra. This result arises because the power spectrum is a slowly varying function of and does not show that, in general, Lorentz boosts can be neglected for other cosmological quantities such as polarization maps or higher-point functions.