DFG-NSF: Investigations on Physical Implications of Canonical Quantum Gravity

量子理论与爱因斯坦广义相对论的统一是理论物理学的主要基本问题之一。尽管在量子引力理论中有各种各样的模型，但基本的问题仍然是如何用量子爱因斯坦方程来表述动力学，以及构建这样一个理论的不同路径是否会导致质量不同的物理预测。没有对这些问题的答案的见解，各种模型及其预测的可靠性仍然是一个悬而未决的问题。这个由美国国家科学基金会资助的奖项旨在解决使用环量子引力技术构建模型中的各种此类问题。一个主要的目标将是探索选择不同的程序来构建模型的物理后果，特别是在宇宙学的设置。该项目的研究将直接影响对重力量化的可靠程序的理解，以及它可能影响物理预测的方式。该项目旨在显著加强路易斯安那州立大学和埃尔兰根-纽伦堡弗里德里希-亚历山大大学研究人员在量子引力基础问题上的合作。这一领域的研究进展将对经典量子引力、经典引力和宇宙学界产生广泛的益处。本项目培养的研究生将有机会进行国际合作。构建量子引力经典理论的两个基本问题是：(1)如何表述量子爱因斯坦方程，(2)理论中的规范固定过程如何与其量子化相交换。利用非平凡的宇宙学模型，该项目旨在探索上述问题的答案。主要目标将是了解在使用环量子引力技术构建模型时所做选择的物理含义，以及它们是否影响任何定性预测，如奇点的分辨率和宇宙扰动。为了克服与量子引力动力学相关的问题，将使用基于狄拉克观测值的关系形式，并将其应用于经典和量子水平的宇宙摄动理论。通过不同路线构建的不同模型之间的关系将被探索，以检验它们的可靠性和结果预测。这项研究有望在理解环量子引力的物理含义方面产生重要的见解，特别是在宇宙学领域。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.