Theoretical systematics in testing the Cosmological Principle with the kinematic quasar dipole

The Cosmological Principle is part of the foundation that underpins the standard model of the Universe. In the era of precision cosmology, when stress tests of the standard model are uncovering various tensions and possible anomalies, it is critical to check the viability of this principle. A key test is the consistency between the kinematic dipoles of the cosmic microwave background and of the large-scale matter distribution. Results using radio continuum and quasar samples indicate a rough agreement in the directions of the two dipoles, but a larger than expected amplitude of the matter dipole. The resulting tension with the radiation dipole has been estimated at $\sim 5\sigma$ for some cases, suggesting a potential new cosmological tension and a possible violation of the CP. However, the standard formalism for predicting the dipole in the two-dimensional projection of sources overlooks possible evolution effects in the luminosity function. In fact, radial information from the luminosity function is necessary for a correct projection of the three-dimensional source distribution. Using a variety of current models of the quasar luminosity function, we show that neglecting redshift evolution can significantly overestimate the relative velocity amplitude. While the models we investigate are consistent with each other and with current data, the dipole derived from these, which depends on derivatives of the luminosity function, can disagree by more than $3\sigma$. This theoretical systematic bias needs to be resolved before robust conclusions can be made about a new cosmic tension.