The effect of dark matter discreteness on light propagation
  Light propagation in cosmology is usually studied in the geometrical optics
approximation which requires the spacetime curvature to be much smaller than
the light wavenumber. However, for non-fuzzy particle dark matter the curvature
is concentrated in widely separated spikes at particle location. If the
particle mass is localised within a Compton wavelength, then for masses
$\gtrsim10^4$ GeV the curvature is larger than the energy of CMB photons.
  We consider a post-geometrical optics approximation that includes curvature.
Photons gain a gravity-induced mass when travelling through dark matter, and
light paths are not null nor geodesic. We find that the correction to the
redshift is negligible. For the angular diameter distance, we show how the
small average density emerges from the large local spikes when integrating
along the light ray. We find that there can be a large correction to the
angular diameter distance even for photon energies much larger than the
curvature. This may allow to set a strong upper limit on the mass of dark
matter particles. We discuss open issues related to the validity of our
approximations.
