  Searches for dispersive effects in the propagation of light at cosmological
distances have been touted as sensitive probes of Lorentz invariance violation
(LIV) and of theories of quantum gravity. Frequency-dependent time lags between
simultaneously emitted pulses of light can signal a modification in the photon
dispersion relation; however, matter engenders the cosmos with a dispersive
index of refraction to similar effect. We construct a theoretical framework for
the analysis of such effects, contrasting these dispersive terms with those
from LIV models. We consider all matter, both luminous and dark. Though the
only known mode of interaction for dark matter (DM) is gravitational, most
models of dark matter also allow for electromagnetic interactions, if only at
the one-loop level in perturbation theory. Generically, the leading order
dispersive effects due to matter scale with photon energy as \omega^{-2} for a
charged DM candidate and \omega^2 for a neutral DM candidate. Terms linear in
\omega can arise in the index of refraction if parity and charge-parity
asymmetries are present at the Lagrangian or system level. Herein, we compute
the index of refraction for a millicharged dark matter candidate at the
one-loop level, a neutral scalar DM candidate introduced by Boehm and Fayet,
and the MSSM's neutralino. For a neutral DM candidate, we determine that matter
effects can compete with LIV effects that depend quadratically on energy
whenever the photon energy is beyond 10^{29} GeV, well beyond the GZK cutoff.
The dispersive matter effects that scale linearly with \omega are model
dependent, and their existence results in circular birefringence.
