A Generalization of Gravity
  I consider theories of gravity built not just from the metric and affine
connection, but also other (possibly higher rank) symmetric tensor(s). The
Lagrangian densities are scalars built from them, and the volume forms are
related to Cayley's hyperdeterminants. The resulting diff-invariant actions
give rise to geometric theories that go beyond the metric paradigm (even
metric-less theories are possible), and contain Einstein gravity as a special
case. Examples contain theories with generalizeations of Riemannian geometry.
The 0-tensor case is related to dilaton gravity. These theories can give rise
to new types of spontaneous Lorentz breaking and might be relevant for "dark"
sector cosmology.
