CAREER: Effective Descriptions of Quantum Systems in Cosmology

Effective equations are a powerful mathematical tool to extract physical phenomena from fundamental quantum theories. Once they have been derived, they show effects at an intuitive level such as in the balance of forces. This is much easier to visualize and compute than the underlying fundamental equations for, e.g., a quantum mechanical wave function. At a general level as well as in key examples, new effective equations will be analyzed and derived systematically in the areas of quantum mechanics, quantum cosmology and quantum gravity. Results will be integrated in the teaching of undergraduate quantum mechanics and of quantum aspects in cosmology such as the emergence of structure in the universe. In new research, the nature of the big bang singularity in quantum cosmology will be analyzed, providing insights into the state of the universe at and before the big bang. Moreover, potentially observable effects of quantum gravity in the early universe and new phenomena in the quantum physics of black holes will be investigated. By focusing on effects rather than the underlying mathematics, comparisons with other approaches to quantum gravity will become possible.

The issues addressed underlie our understanding of the universe and typically attract wide interest. New methods to be introduced make implications of quantum gravity accessible for the non-specialist and bridge the traditional gap between fundamental research in this area and cosmological phenomenology. In this way, key infrastructure will be made available to other researchers, and manageable projects to guide students to the field will be generated. By integrating new methods and results into teaching at early stages, the understanding of quantum physics will be improved. Modern examples of applications in cosmology, an area of interest to many students, will provide additional motivation. Specific results will regularly be disseminated

to the research community and the general public.