Cosmological parameter estimation: impact of CMB aberration

Abstract

The peculiar motion of an observer with respect to the CMB rest frame induces an apparent deflection of the observed CMB photons, {\it i.e.} aberration, and a shift in their frequency, {\it i.e.} Doppler effect. Both effects distort the temperature multipoles $a_{\ell m}$'s via a mixing matrix at {\it any} $\ell$. The common lore when performing a CMB based cosmological parameter estimation is to consider that Doppler affects only the $l=1$ multipole, and neglect any other corrections. In this paper we check the validity of this assumption in parameter estimation for a Planck-like angular resolution, both for a full-sky ideal experiment and also when sky cuts are included to model CMB foreground contaminations with a sky fraction similar to the Planck satellite. Assuming a simple fiducial cosmological model with five parameters, we simulated CMB temperature maps of the sky and added aberration and Doppler effects to the maps. We then analyzed with a MCMC in a Bayesian framework the maps with and without aberration and Doppler effects in order to assess the ability of reconstructing the parameters of the fiducial model. Although the correction on the power spectrum $C_{\ell }$ is larger than the cosmic variance at $\ell >1000$ and potentially important, we find that the bias on the parameters is negligible for Planck.

17 pages, 4 figures. Corrected a numerical error, main conclusion modified

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• Bayesian estimation of our local motion from the Planck-2018 CMB temperature map
• New operator approach to the CMB aberration kernels in harmonic space
• CMB Aberration and Doppler Effects as a Source of Hemispherical Asymmetries
• Statistical Anisotropic Gaussian Simulations of the CMB Temperature Field
• Disentangling Doppler modulation, aberration and the temperature dipole in the CMB
• Real Space Approach to CMB deboosting
• CMB all-scale blackbody distortions induced by linearizing temperature
• CMB all-scale blackbody distortions induced by linearizing temperature
• A Generalized Doppler and Aberration Kernel for Frequency-Dependent Cosmological Observables
• Footprints of Doppler and Aberration Effects in CMB Experiments: Statistical and Cosmological Implications
• Non-Gaussianity and CMB aberration and Doppler
• Determining our peculiar velocity from the aberration in the cosmic microwave background
• Effects of boosting on extragalactic components: methods and statistical studies