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. However, the majority of known mathematical methods are insufficient for a complete analysis of a combination of these theories, or quantum gravity. Fascinating phenomena such as the very first stages of the big bang or the cores of black holes therefore remain out of reach for our current understanding. This project promotes the progress of science by deriving new methods and investigating systems in which both general relativity and quantum mechanics are relevant. Applications to mathematical models of the big bang and black holes will lead to conclusions that are of interest to the public at large. They further our knowledge about the universe, for instance by providing new tests of general relativity for strong gravitational fields. Methods derived in this project can also be used for systems that do not involve general relativity, where they may help to solve technical questions or to communicate results in a new way. The project therefore supports education, for instance in teaching quantum mechanics. This project also supports diversity by including undergraduate and graduate students from underrepresented groups.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. They are therefore 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 some of the main problems of quantum gravity. During this funding period emphasis will be put on understanding implications of possible non-associative structures in quantum physics, as well as non-classical space-time effects around black holes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.