Early Universe Dynamics in Semi-Classical Loop Quantum Cosmology
  Within the framework of loop quantum cosmology, there exists a semi-classical regime where spacetime may be approximated in terms of a continuous manifold, but where the standard Friedmann equations of classical Einstein gravity receive non-perturbative quantum corrections. An approximate, analytical approach to studying cosmic dynamics in this regime is developed for both spatially flat and positively-curved isotropic universes sourced by a self-interacting scalar field. In the former case, a direct correspondence between the classical and semi-classical field equations can be established together with a scale factor duality that directly relates different expanding and contracting universes. Some examples of non-singular, bouncing cosmologies are presented together with a scaling, power-law solution. 
James E. Lidsey