Dark Matter from a Dark Connection
  In the first part of this note, we observe that a non-Riemannian piece in the
affine connection (a "dark connection") leads to an algebraically determined,
conserved, symmetric 2-tensor in the Einstein field equations that is a natural
dark matter candidate. The only other effect it has, is through its coupling to
standard model fermions via covariant derivatives. If the local dark matter
density is the result of a background classical dark connection, these
Yukawa-like mass corrections are minuscule ($\sim 10^{-31}$ eV for terrestrial
fermions) and {\em none} of the tests of general relativity or the equivalence
principle are affected. In the second part of the note, we give dynamics to the
dark connection and show how it can be re-interpreted in terms of conventional
dark matter particles. The simplest way to do this is to treat it as a
composite field involving scalars or vectors. The (pseudo-)scalar model
naturally has a perturbative shift-symmetry and leads to versions of the Fuzzy
Dark Matter (FDM) scenario that has recently become popular (eg.,
arXiv:1610.08297) as an alternative to WIMPs. A vector model with a ${\cal
Z}_2$-parity falls into the Planckian Interacting Dark Matter (PIDM) paradigm,
introduced in arXiv:1511.03278. It is possible to construct versions of these
theories that yield the correct relic density, fit with inflation, and are
falsifiable in the next round of CMB experiments. Our work is an explicit
demonstration that the meaningful distinction is not between gravity
modification and dark matter, but between theories with extra fields and those
without.
