I consider symmetries which could explain observed properties of dark matter,
namely, its stability on Gyr time scales or its relic density and discuss how
such symmetries can be discovered through the study of the propagation and
polarization of light in its transit through dark matter.Comment: 6 pages, Invited talk at the 4th International Symposium on
Symmetries in Subatomic Physics (SSP 2009), June 2-5, 2009, Taipei, Taiwa