  Suppose the usual description of spacetime as a 4-dimensional manifold with a
Lorentzian metric breaks down at Planck energies. Can we still construct
sensible theoretical models of the universe? Are they testable? Do they lead to
a consistent quantum cosmology? Is this cosmology different than the standard
one? The answer is yes, to all these questions, assuming that quantum theory is
still valid at this scale. I describe the basic features of such models, mainly
quantum causal histories and spin foams. They are given by a partition
function, similar to spin systems and lattice gauge theories. This suggests
that we should treat this approach to quantum gravity as a problem in
statistical physics, but with significant complications: there is no background
and, in particular, no external time. Gravity and the familiar 3+1 manifold
spacetime are to be derived as the low-energy continuum approximation to these
models.
