  General relativity promotes space-time to a physical, dynamical object
subject to equations of motion. Quantum gravity, accordingly, must provide a
quantum framework for space-time, applicable on the smallest distance scales.
Just like generic states in quantum mechanics, quantum space-time structures
may be highly counter-intuitive. But if low-energy effects can be extracted,
they shed considerable light on the implications to be expected for a dynamical
quantum space-time. Loop quantum gravity has provided several such effects, but
even in the symmetry-reduced setting of loop quantum cosmology no complete
picture of effective space-time geometries describing especially the regime
near the big bang has been obtained. The overall situation regarding space-time
structures and cosmology is reviewed here, with an emphasis on the role of
dynamical states, effective equations, and general covariance.
