In the concordance model of the Universe, the matter distribution - as
observed in galaxy number counts or the intensity of line emission (such as the
21cm line of neutral hydrogen) - should have a kinematic dipole due to the
Sun's motion relative to the CMB rest-frame. This dipole should be aligned with
the kinematic dipole in the CMB temperature. Accurate measurement of the
direction of the matter dipole will become possible with future galaxy surveys,
and this will be a critical test of the foundations of the concordance model.
The amplitude of the matter dipole is also a potential cosmological probe. We
derive formulas for the amplitude of the kinematic dipole in galaxy redshift
and intensity mapping surveys, taking into account the Doppler, aberration and
other relativistic effects. The amplitude of the matter dipole can be
significantly larger than that of the CMB dipole. Its redshift dependence
encodes information on the evolution of the Universe and on the tracers, and we
discuss possible ways to determine the amplitude.