Galaxy number-count dipole and superhorizon fluctuations

In view of the growing tension between the dipole anisotropy of number counts of cosmologically distant sources and of the cosmic microwave background (CMB), we investigate the number count dipole induced by primordial perturbations with wavelength comparable to or exceeding the Hubble radius today. First, we find that neither adiabatic nor isocurvature superhorizon modes can generate an intrinsic number count dipole. However a superhorizon isocurvature mode does induce a relative velocity between the CMB and the (dark) matter rest frames and thereby affects the CMB dipole. We revisit the possibility that it has an intrinsic component due to such a mode, thus enabling consistency with the galaxy number count dipole if the latter is actually kinematic in origin. Although this scenario is not particularly natural, there are possible links with other anomalies and it predicts a concommitant galaxy number count quadrupole which may be measurable in future surveys. We also investigate the number count dipole induced by modes smaller than the Hubble radius, finding that subject to CMB constraints this is too small to reconcile the dipole tension.