Effective Descriptions of Quantum Gravity and Cosmology

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General relativity and quantum mechanics are the two major theories that govern fundamental physics, of space-time and of elementary particles. However, it is not known how they could be combined to a consistent theory of quantum gravity. Fascinating phenomena such as the very first stages of the big bang or the cores of black holes therefore remain out of the reach of our current understanding. This project investigates a wide range of systems in which both general relativity and quantum mechanics are relevant. The main interest is given by methods that allow one to derive physical implications by approximations, and to use the results to guide the developments of quantum gravity. Applications to the big bang and black holes often lead to conclusions that capture the interest of the general public. Related methods can also be used in systems not involving general relativity, where they may help to solve technical questions or to communicate results in a new way, supporting for instance the teaching of quantum mechanics.The objective of this project is to introduce and evaluate new methods for a systematic analysis of physical implications of one set of candidate theories of quantum gravity, based on canonical quantization. Throughout physics, a powerful tool to derive potentially observable phenomena is given by effective theories which provide quantum corrections to the classical equations. Such systems can more easily be evaluated, analytically or numerically, than equations for quantum states and thus are more direct sources for the discovery of new phenomena. While standard techniques to derive effective equations do not apply to canonical quantum gravity, a general scheme applicable to canonical quantum theories exists (introduced by the PI) and is used in this project to address the main problems of quantum gravity. It provides the basis for a long-term program evaluating physical phenomena in the broad context of quantum gravity. Such a systematic derivation will make it possible to put effects found previously in simplified models on a firm footing, uncover new phenomena and provide reliable predictions. Results will be used to compare the theory with other candidates of quantum gravity, with the potential of a fruitful transfer of ideas and techniques between the approaches.