is the effective space-time description of the underlying quantum evolution. The effective dynamics approach has been extensively used in loop quantum cosmology to describe physics at the Planck scale and the very early universe. Rigorous numerical simulations have confirmed the validity of the effective dynamics, which provides an excellent approximation to the full loop quantum dynamics. It has been shown that only when the states have very large quantum fluctuations at late times, which means that they do not lead to macroscopic universes as described by general relativity, that the effective dynamics has departures from the quantum dynamics near bounce and the subsequent evolution. In such a case, the effective dynamics overestimates the density at the bounce, but still captures the qualitative aspects extremely well. Scale-invariant loop quantum cosmology If the underlying spacetime geometry with matter has a scale invariance, which has been proposed to resolve the problem of time, Immirzi ambiguity and hierarchy problem of fundamental couplings, then the resulting loop quantum geometry has no definitive discrete gaps or a minimum size. Consequently, in scale-invariant LQC, the Big Bang is shown not to be replaced by a quantum bounce. See also Canonical quantum gravity Dilaton References External links Loop quantum cosmology on arxiv.org Quantum Nature of The Big Bang in Loop Quantum Cosmology Gravity and the Quantum Loop Quantum Cosmology, Martin Bojowald Did our cosmos exist before the Big Bang? Abhay Ashtekar, Parampreet Singh "Loop Quantum Cosmology: A Status Report" Physical cosmology Loop quantum gravity