On the kinematic cosmic dipole tension
  Our motion through the Universe generates a dipole in the temperature
anisotropies of the Cosmic Microwave Background (CMB) and also in the angular
distribution of sources. If the cosmological principle is valid, these two
dipoles are directly linked, such that the amplitude of one determines that of
the other. However, it is a longstanding problem that number counts of radio
sources and of quasars at low and intermediate redshifts exhibit a dipole that
is well aligned with that of the CMB but with about twice the expected
amplitude, leading to a tension reaching up to $4.9 \sigma$. In this paper, we
revisit the theoretical derivation of the dipole in the sources number counts,
explicitly accounting for the redshift evolution of the population of sources.
We argue that if the spectral index and magnification bias of the sources vary
with redshift, the standard theoretical description of the dipole may be
inaccurate. We provide an alternative expression which does not depend on the
spectral index, but instead on the time evolution of the population of sources.
We then determine the values that this evolution rate should have in order to
remove the tension with the CMB dipole.
