The median density of the Universe
  Despite the fact that the mean matter density of the universe has been
measured to an accuracy of a few percent within the standard $\Lambda$CDM
paradigm, its median density is not known even to order of magnitude. Typical
points lie in low-density regions and are not part of a collapsed structure of
any scale. Locally, the dark matter distribution is then simply a stretched
version of that in the early universe. In this single-stream regime, the
distribution of unsmoothed density is sensitive to the initial power spectrum
on all scales, in particular on very small scales, and hence to the nature of
the dark matter. It cannot be estimated reliably using conventional
cosmological simulations because of the enormous dynamic range involved, but a
suitable excursion set procedure can be used instead. For the Planck
cosmological parameters, a 100 GeV WIMP, corresponding to a free-streaming mass
$\sim 10^{-6}M_\odot$, results in a median density of $\sim 4\times 10^{-3}$ in
units of the mean density, whereas a 10 $\mu$eV axion with free-streaming mass
$\sim 10^{-12}M_\odot$ gives $\sim 3\times 10^{-3}$, and Warm Dark Matter with
a (thermal relic) mass of 1 keV gives $\sim 8\times 10^{-2}$. In CDM (but not
in WDM) universes, single-stream regions are predicted to be topologically
isolated by the excursion set formalism. A test by direct N-Body simulations
seems to confirm this prediction, although it is still subject to finite size
and resolution effects. Unfortunately, it is unlikely that any of these
properties is observable and so suitable for constraining the properties of
dark matter.
