Spacetime and dark matter from spontaneous breaking of Lorentz symmetry
  It is shown that a spontaneously-broken gauge theory of the Lorentz group
contains Ashtekar's chiral formulation of General Relativity accompanied by
dust. From this perspective, gravity is described entirely by a connection
$\omega$ valued in the Lie algebra of the complexified Lorentz group and a
Lorentz-charged scalar field $\tau$. The model is "pre-geometric" in the sense
that the spacetime metric may be constructed only in the symmetry-broken
regime. We speculate on the extent to which this dust may account for dark
matter and on the behaviour of the theory in regimes where the symmetry is not
broken.
