The High-Altitude Water Cherenkov Gamma Ray Observatory (HAWC) is designed to perform a synoptic survey of the TeV sky. The high energy coverage of the experiment will enable studies of fundamental physics beyond the Standard Model, and the large field of view of the detector will enable detailed studies of cosmologically significant backgrounds and magnetic fields. We describe the sensitivity of the full HAWC array to these phenomena in five contributions shown at the 33rd International Cosmic Ray Conference in Rio de Janeiro, Brazil (July 2013).