  The predicted size of dark matter substructures in kilo-parsec scales is
model-dependent. Therefore, if the correlations between dark matter mass
densities as a function of the distances between them are measured via
observations, we can scrutinize dark matter scenarios. In this paper, we
present an assessment procedure of dark matter scenarios. First, we use Gaia's
data to infer the single-body phase-space density of the stars in the Fornax
dwarf spheroidal galaxy. The latter, together with the Jeans equation, after
eliminating the gravitational potential using the Poisson equation, reveals the
mass density of dark matter as a function of its position in the galaxy. We
derive the correlations between dark matter mass densities as a function of
distances between them. No statistically significant correlation is observed.
Second, for the sake of comparison with the standard cold dark matter, we also
compute the correlations between dark matter mass densities in a small halo of
the Eagle hydrodynamics simulation. We show that the correlations from the
simulation and from Gaia are in agreement. Third, we show that Gaia
observations can be used to limit the parameter space of the Ginzburg--Landau
statistical field theory of dark matter mass densities and subsequently shrink
the parameter space of any dark matter model. As two examples, we show how to
leave limitations on (i) a classic gas dark matter and (ii) a superfluid dark
matter.
