Seminarium Teorii Względności i Grawitacji

Quantum cosmology offers the possibility to study some of the conceptual questions of quantum gravity in a simplified setting. In the simplest case, homogeneous and isotropic general relativity coupled to a massless scalar field, the quantum theory turns out to be exactly soluble. We review some results of Ashtekar, Corichi, and Singh (arXiv:0710.3565), enriched with some clarifications on the choice of scalar products based on work by Kaminski, Lewandowski, and Pawlowski (arXiv:0907.4322). The involved computations neatly show the origin of the singularity resolution mechanism of loop quantum cosmology as opposed to the standard Wheeler-de Witt theory. This talk is mainly intended as a pedagogical review of (other people's) interesting results.