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The predicted size of dark matter substructures in kilo-parsec scales ismodel-dependent. Therefore, if the correlations between dark matter massdensities as a function of the distances between them are measured viaobservations, we can scrutinize dark matter scenarios. In this paper, wepresent an assessment procedure of dark matter scenarios. First, we use Gaia'sdata to infer the single-body phase-space density of the stars in the Fornaxdwarf spheroidal galaxy. The latter, together with the Jeans equation, aftereliminating the gravitational potential using the Poisson equation, reveals themass density of dark matter as a function of its position in the galaxy. Wederive the correlations between dark matter mass densities as a function ofdistances between them. No statistically significant correlation is observed.Second, for the sake of comparison with the standard cold dark matter, we alsocompute the correlations between dark matter mass densities in a small halo ofthe Eagle hydrodynamics simulation. We show that the correlations from thesimulation and from Gaia are in agreement. Third, we show that Gaiaobservations can be used to limit the parameter space of the Ginzburg--Landaustatistical field theory of dark matter mass densities and subsequently shrinkthe parameter space of any dark matter model. As two examples, we show how toleave limitations on (i) a classic gas dark matter and (ii) a superfluid darkmatter.

Assessment of Dark Matter Models Using Dark Matter Correlations across Dwarf Spheroidal Galaxies