Loop Quantum Gravity with Cosmological Constant

众所周知，爱因斯坦的广义相对论（GR）是描述引力物理的理论。广义相对论帮助我们在理解空间和时间的基本方面取得了许多巨大的进步。该理论成功地描述了宇宙的物理性质，并对各种天体物理现象做出了预测。然而，众所周知，GR理论是不完整的。它失去了在极其强大的引力场中进行预测的能力，例如在黑洞内部，或者在宇宙大爆炸的早期阶段。物理学中最基本的开放问题之一是如何完成GR以预测极强引力场中的物理。我们正在寻找的完整引力理论被称为“量子引力”。量子引力理论在描述黑洞内部的物理现象，帮助我们理解大爆炸附近的早期宇宙方面应该发挥至关重要的作用。最终，量子引力将引导我们对空间和时间进行革命性的理解。PI小组还将在STEM研究领域培训学生。该奖项支持被称为“环量子引力”（LQG）理论的发展。LQG是一种研究量子引力的方法，具有背景无关性和时空结构的非摄动量子化的特点。在发展LQG理论的过程中，PI提出了一个具有宇宙学常数的LQG的新公式。新公式定义了LQG的有限自旋振幅。它还将LQG与物理学和数学的许多其他分支联系起来，特别是指出了LQG与弦/ m理论之间的具体关系。带宇宙常数的LQG的新公式将在这个项目中得到充分的探索，希望在宇宙学的一些开放问题上取得进展。建议的工作旨在(1)完成新模型的非摄动和摄动公式；(2)通过探索与String/ m理论和AdS/CFT的关系，获得LQG的新见解和新工具；(3)提取宇宙常数物理的现象学预测。该项目有望成为构建可进行实证检验的LQG完整公式的重要一步。

It is known that Einstein's General Relativity (GR) is theory to describe the gravitational physics. The theory of GR has helped us to make many tremendous progresses in understanding the fundamental aspect of space and time. The theory has been successful in describing the physics of universe, as well as making predictions for various astrophysical phenomena. However it is also well-known that the theory of GR is incomplete. It loses its capability of making predictions in the extremely strong gravitational field, e.g. inside a black hole, or at the very early stage of universe near the big bang. One of the most fundamental open questions in physics is how to complete GR in order to predict physics in an extremely strong gravitational field. The complete theory of gravity that we are searching for is called "Quantum Gravity". The theory of Quantum Gravity should play a crucial role in describing the physics inside black hole, and helping us to understand the early universe near the big bang. Eventually Quantum Gravity will lead us to a revolutionary understanding of space and time. The PI's group will also train students in STEM areas of research.This award support the development of a the theory of known as "Loop Quantum Gravity" (LQG). LQG is an approach toward Quantum Gravity featured with the background independence and non-perturbative quantization of spacetime structure. In developing the theory of LQG, the PI presented a promising new formulation of LQG with a cosmological constant. The new formulation defines finite spinfoam amplitudes of LQG. It also relates LQG to many other branches of physics and mathematics, in particular, it points out a concrete relation between LQG and String/M-Theory. The new formulation of LQG with a cosmological constant is going to be fully explored in this project, hopefully making progress towards some open issues in cosmology. The proposed work aims at (1) completing both the non-perturbative and perturbative formulation of the new model; (2) obtaining new insights and tools for LQG by exploring the relation to String/M-Theory and AdS/CFT; (3) extracting phenomenological predictions on the physics of cosmological constant. This project is expected to be an important step toward a complete formulation of LQG that could be empirically tested.