The effect of dark matter discreteness on light propagation

Abstract

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 ≳104 GeV the curvature is larger than the energy of CMB photons.We consider a post-geometrical optics approximation that includescurvature. Photons gain a gravity-induced mass when travelling throughdark matter, and light paths are not null nor geodesic. We find thatthe correction to the redshift is negligible. For the angular diameterdistance, we show how the small average density emerges from the largelocal spikes when integrating along the light ray. We find that therecan be a large correction to the angular diameter distance even forphoton energies much larger than the curvature. This may allow to seta strong upper limit on the mass of dark matter particles. We discussopen issues related to the validity of our approximations.