  We initiate the study of dark matter models based on a gapped continuum. Dark
matter consists of a mixture of states with a continuous mass distribution,
which evolves as the universe expands. We present an effective field theory
describing the gapped continuum, outline the structure of the Hilbert space and
show how to deal with the thermodynamics of such a system. This formalism
enables us to study the cosmological evolution and phenomenology of gapped
continuum DM in detail. As a concrete example, we consider a weakly-interacting
continuum (WIC) model, a gapped continuum counterpart of the familiar WIMP. The
DM interacts with the SM via a Z-portal. The model successfully reproduces the
observed relic density, while direct detection constraints are avoided due to
the effect of continuum kinematics. The model has striking observational
consequences, including continuous decays of DM states throughout cosmological
history, as well as cascade decays of DM states produced at colliders. We also
describe how the WIC theory can arise from a local, unitary scalar QFT
propagating on a five-dimensional warped background with a soft wall.
