Planck-scale Models of the Universe

Suppose the usual description of spacetime as a 3+1 manifold breaks down at the scale where a quantum theory of gravity is expected to describe the world, generally agreed to be the Planck scale, lp = 10 m. 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. After eighty years work on quantum gravity, we do have the first detailed models for the microscopic structure of spacetime: spin foams. The first spin foam models were based on the predictions of loop quantum gravity, namely the quantization of general relativity, for the quantum geometry at Planck scale. A main result of loop quantum gravity is that the quantum operators for spatial areas and volumes have discrete spectra. Discreteness is central to spin foams, which are discrete models of spacetime at Planck scale. Several more models have been proposed since, based on results from other approaches to quantum gravity, such as Lorentzian