Singularity Resolution in Quantum Gravity

众所周知，当引力场变得足够强大时，爱因斯坦的广义相对论就会瓦解（变得奇异）。宇宙大爆炸就是一个例子。在原子尺度上，类似的电磁学故障可以通过转换到遵循量子力学原理的理论来解决。人们希望量子引力理论能消除广义相对论中的奇点。在该奖项下进行的研究旨在提供新的见解和发现新的方向，以回答有关这些奇点的移除（或解决）的基本问题。将系统地考虑量子引力效应，以理解宇宙和黑洞时空中的奇点是如何被解决的。通过建立在量子宇宙学（简单模型宇宙的量子化）的基础上，对更复杂模型的研究将被执行，其目标是对量子引力中奇点的一般分辨率产生见解。将建立现象学模型来理解量子引力效应在宇宙学情景中的广泛分支。该研究的另一个目标将是解决量子宇宙学中的相关基础问题，例如在量子宇宙中分配事件概率的一致方法。这项研究将导致在量子引力（普朗克）尺度上对新物理学的更深入的理解，这将对量子引力、宇宙学和其他物理学领域产生广泛的影响。在不同模型下对奇点分辨率的研究将为完整的量子引力理论提供有用的线索。该NSF奖还将导致研究生的培训，从而对他/她的研究生涯产生长期影响。在该奖项中获得的成果将通过撰写学术文章和在会议和讲习班上举办研讨会的方式传播给科学界。本奖项所涉及的基本问题也涉及公众的广泛利益。结果将以各种方式向公众传播，包括向环量子引力网站投稿。

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.