The expected kinematic matter dipole is robust against source evolution

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 $\mathrm{\Lambda }$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 $>5\sigma$ dipole anomaly uncovered recently remains an outstanding challenge to the $\mathrm{\Lambda }$CDM model.