Universe scenarios from loop quantum cosmology
  Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of spatial geometry entail physical consequences for the structure of classical singularities as well as the evolution of the very early universe. While the singularity issue in general requires one to use difference equations for a wave function of the universe, phenomenological scenarios for the evolution are based on effective equations implementing the main quantum modifications. These equations show generic bounces as well as inflation in diverse models, which have been combined to more complicated scenarios. 
Martin Bojowald