Singularity Resolution in Quantum Gravity

当引力场变得足够强时，爱因斯坦的广义相对论就会崩溃（变得奇异）。宇宙大爆炸就是一个例子。电磁学在原子尺度上的类似崩溃通过转向遵循量子力学原理的理论而得到治愈。人们希望引力的量子理论能消除广义相对论中的奇点。该奖项下进行的研究旨在提供新的见解，并发现新的方向，以回答关于去除（或解决）这些奇点的基本问题。量子引力效应将被系统地考虑，以理解宇宙学和黑洞时空中奇点的解决方式。通过建立在量子宇宙学（简单模型宇宙的量子化）的基础上，将对更复杂的模型进行研究，目的是深入了解量子引力中奇点的一般分辨率。将建立唯象模型来理解宇宙学场景中量子引力效应的广泛分支。该研究的另一个目标是解决量子宇宙学中的相关基础问题，例如量子宇宙中事件概率的一致性分配方法。这项研究将加深对量子引力（普朗克）尺度下新物理学的理解，这将对量子引力、宇宙学和其他物理学领域产生广泛影响。对不同模型下奇异性分辨的研究将为量子引力的完整理论提供有益的启示。这个NSF奖也将导致一个研究生的培训，导致他/她的研究生涯的长期影响。在这个奖项中获得的成果将通过撰写学术文章和在会议和研讨会上举办研讨会的方式传播给科学界。该奖项所涉及的基本问题也引起了公众的广泛兴趣。结果将以各种方式向公众传播，包括对圈量子引力网站的贡献。

Einstein's theory of General Relativity is known to break down (become singular) when gravitational fields become sufficiently strong. The Big Bang is an example. A similar breakdown in electromagnetism on the atomic scale is cured by switching to a theory that obeys the principles of quantum mechanics. It is hoped that a quantum theory of gravity will remove the singularities in General Relativity. The research performed under this award aims to provide new insights and discover novel directions to answer fundamental questions on the removal (or resolution) of these singularities. Quantum gravitational effects will be systematically taken into account to understand the way singularities in cosmological and black hole spacetimes are resolved. By building on quantum cosmology (the quantization of simple model universes), investigations on more complex models will be performed with the goal of yielding insights on the generic resolution of singularities in quantum gravity. Phenomenological models will be built to understand broad ramifications of the quantum gravity effects in the cosmological scenarios. Another goal of the research will to be address related foundational issues in quantum cosmology, such as a consistent way to assign probabilities for events in a quantum universe.This research will lead to deeper understanding of the new physics at the quantum gravity (Planck) scale that will have broad implications for quantum gravity, cosmology and other areas of physics. The research on singularity resolution in different models will provide useful hints on the full theory of quantum gravity. This NSF award will also lead to a training of a graduate student leading to a long term impact on his/her research career. Results obtained in this award will be disseminated to the scientific community by writing scholarly articles and seminars in conferences and workshops. The fundamental questions addressed in this award also have broad interest of the general public. Results will be disseminated to the public in various ways including contributions to the loop quantum gravity website.