The effect of dark matter discreteness on light propagation

TL;DR

This paper investigates how the discrete nature of dark matter particles affects light propagation, revealing potential large corrections to angular diameter distance that could constrain dark matter particle mass.

Contribution

It introduces a post-geometrical optics approximation accounting for dark matter discreteness, showing significant effects on light propagation not captured by standard models.

Findings

Negligible correction to redshift from dark matter discreteness

Small average density emerges from local spikes in dark matter

Large correction to angular diameter distance possible, constraining dark matter mass

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 $\gtrsim10^4$ 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.