  Dark matter is one of the deepest mystery of the universe. So far there is no
natural explanation why the dark matter should exist and even dominate the
universe. In this paper, we begin with a 3+1D topological gravity theory which
is super renormalizable with vanishing beta functions, then we argue that
Einstein gravity can emerge by condensing loop-like excitation from the
underlying topological gravity theory. In the meanwhile, the uncondensed
loop-like excitations serves as a natural candidate of dark matter and a
generalized Einstein equation can be derived in the presence of
loop-source(dark matter) background. Surprisingly, we find that such kind of
dark matter will not contribute to scalar curvature, however, it will become a
source of torsion. Finally, we derive the generalized Einstein equation in the
presence of Dirac field. Very different from the usual Einstein-Carton theory,
our theory further predicts that any type of normal matter, including Dirac
field will not produce torsion. All these unique predictions can be tested by
future experiments. Our framework suggests that topological invariant principle
might play a more profound role than the well-known general covariance
principle, especially towards understanding the nature of dark matter and
quantum gravity in 3+1D.
