The unification of quantum theory and Einstein's theory of general relativity is one of the main fundamental problems of theoretical physics. Despite the availability of various models in the quantum theory of gravity, fundamental questions remain on how to formulate dynamics in terms of quantum Einstein equations, and if different paths to construct such a theory result in qualitatively different physical predictions. Without insights on answers to these questions, the reliability of various models and their predictions remains an open issue. This NSF funded award aims to address various such questions in construction of models using techniques of loop quantum gravity. A primary objective will be to explore the physical consequences of choosing different procedures to construct models, especially in the cosmological setting. Research in this project will have direct implications for the understanding of a reliable procedure to quantize gravity and the way it can potentially impact physical predictions. The project aims to significantly enhance collaboration on fundamental issues in quantum gravity between researchers at Louisiana State University and at Friedrich-Alexander University at Erlangen-Nuremberg. Progress in this area of research will have broad benefit for canonical quantum gravity, classical gravity and cosmology communities. Graduate students trained in this project will have opportunities for international collaboration.
Two fundamental problems in the construction of a canonical theory of quantum gravity are: (i) how to formulate quantum Einstein equations, and (ii) how does the procedure of gauge fixing in the theory commute with its quantization. Using non-trivial cosmological models, this project aims to explore answers to the above questions. The primary goal will be to understand the physical implications of the choices made in the construction of models using techniques of loop quantum gravity, and whether they affect any qualitative predictions such as resolution of singularities and for cosmological perturbations. To overcome the problems associated with dynamics in quantum gravity, a relational formalism based on Dirac observables will be used and applied to cosmological perturbation theory both at the classical and quantum levels. The relationship between different models constructed via different routes will be explored to test their reliability and resulting predictions. This research is expected to yield significant insights on understanding the physical implications of loop quantum gravity, especially in the cosmological sector.
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.