We present exact kinematic consistency relations for cosmological structures
that do not vanish at equal times and can thus be measured in surveys. These
rely on cross-correlations between the density and velocity, or momentum,
fields. Indeed, the uniform transport of small-scale structures by long
wavelength modes, which cannot be detected at equal times by looking at density
correlations only, gives rise to a shift in the amplitude of the velocity field
that could be measured. These consistency relations only rely on the weak
equivalence principle and Gaussian initial conditions. They remain valid in the
non-linear regime and for biased galaxy fields. They can be used to constrain
non-standard cosmological scenarios or the large-scale galaxy bias.Comment: 5 page
