Measuring our peculiar velocity on the CMB with high-multipole off-diagonal correlations

TL;DR

This paper proposes a method to measure our local velocity relative to the CMB using high-multipole off-diagonal correlations, providing a cross-check for the origin of the CMB dipole and testing for preferred directions.

Contribution

It introduces a novel approach to independently determine our velocity from CMB anisotropies using off-diagonal correlations at high multipoles.

Findings

Planck can measure velocity with about 30% error.

The method can determine the velocity direction within approximately 20 degrees.

It offers a way to distinguish between velocity-induced and intrinsic sources of the CMB dipole.

Abstract

Our peculiar velocity with respect to the CMB rest frame is known to induce a large dipole in the CMB. However, the motion of an observer has also the effect of distorting the anisotropies at all scales, as shown by Challinor and Van Leeuwen (2002), due to aberration and Doppler effects. We propose to measure independently our local motion by using off-diagonal two-point correlation functions for high multipoles. We study the observability of the signal for temperature and polarization anisotropies. We point out that Planck can measure the velocity $\beta$ with an error of about 30% and the direction with an error of about 20 degrees. This method constitutes a cross-check, which can be useful to verify that our CMB dipole is due mainly to our velocity or to disentangle the velocity from other possible intrinsic sources. Although in this paper we focus on our peculiar velocity, a similar effect would result also from other intrinsic vectorial distortion of the CMB which would induce a dipolar lensing. Measuring the off-diagonal correlation terms is therefore a test for a preferred direction on the CMB sky.