Quantum Cosmology ∗

Synopsis: Quantum cosmology in general denotes the application of quantum physics to the whole universe and thus gives rise to many realizations and examples, covering problems at different mathematical and conceptual levels. It is related to quantum gravity and more specifically describes the application to cosmological situations rather than the construction and analysis of quantum field equations. As there are several different approaches to quantum gravity, equations for quantum cosmology are not unique. Most investigations have been performed in the context of canonical quantization, where Wheeler–DeWitt like equations are the prime object. Applications are mostly conceptual, ranging from possible resolutions of classical singularities and explanations of the uniqueness of the universe to the origin of seeds for a classical world and its initial conditions.