The expected kinematic matter dipole is robust against source evolution

ABSTRACT Recent measurements using catalogues of quasars and radio galaxies have shown that the dipole anisotropy in the large-scale distribution of matter is about twice as large as is expected in the standard lambda cold dark matter ($\Lambda$CDM) model, indeed in any cosmology based on the Friedman–Lemaître–Robertson–Walker (FLRW) metric. This expectation is based on the kinematic interpretation of the dipole anisotropy of the cosmic microwave background, i.e. as arising due to our local peculiar velocity. The effect of aberration and Doppler boosting on the projected number counts on the sky of cosmologically distant objects in a flux-limited catalogue can then be calculated and confronted with observations. This fundamental consistency test of FLRW models proposed by Ellis & Baldwin in 1984 was revisited recently arguing that redshift evolution of the sources can significantly affect the expected matter dipole. In this note, we demonstrate that the Ellis & Baldwin test is in fact robust to such effects, hence the $\gt 5\sigma$ dipole anomaly uncovered recently remains an outstanding challenge to the $\Lambda$CDM model.