Loop Quantum Gravity with Cosmological Constant

爱因斯坦的广义相对论（GR）是描述经典引力场物理学的理论。广义相对论在理解空间和时间的基本方面取得了巨大的进步，并成功地预测了宇宙的演化和各种天体物理现象。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，例如在黑洞内部或在宇宙大爆炸附近的早期阶段。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”。量子引力理论应该在描述黑洞内部的物理和帮助我们理解大爆炸附近的早期宇宙方面发挥关键作用。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。该奖项支持被称为“环量子引力”（LQG）的候选量子引力理论的发展，它为解决所提出的问题提供了重要的希望。该奖项支持的工作重点是发展具有四维宇宙学常数的LQG理论，特别是理论的旋转信息公式。该项目的主要目标是：(1)研究理论的连续统极限，特别是从自旋信息振幅中出现的光滑时空几何和爱因斯坦方程，并将自旋信息公式与最近从量子信息中出现的引力程序联系起来；(2)在自旋信息框架中分析曲率奇点的量子效应，并提取物理观测值；(3)建立一个与宇宙常数的spinfoam公式密切相关的规范框架。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。

Einstein's General Relativity (GR) is the theory describing the physics of the classical gravitational field. The theory of GR has made tremendous progress in understanding the fundamental aspects of space and time and has been successful in making predictions for the evolution of the universe and various astrophysical phenomena. However it is well-known that the theory of GR is incomplete. It loses its capability of making predictions in extremely strong gravitational fields, e.g. inside a black hole or at the very early stage of the 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 holes 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. This award supports the development of a candidate Quantum Gravity theory known as "Loop Quantum Gravity" (LQG), which offers significant promise in addressing the questions posed. The work supported by this award focuses on developing the theory of LQG with a cosmological constant in 4 dimensions, in particular the spinfoam formulation of theory. The main objectives of this project are: (1) Investigating the continuum limit of the theory, in particular the emergence of smooth spacetime geometries and Einstein equations from the spinfoam amplitude, and relating the spinfoam formulation to the recent program of emergent gravity from quantum information, (2) analyzing the quantum effects of curvature singularities in the framework of spinfoams, and to extract physical observables, and (3) developing a canonical framework closely related to the spinfoam formulation with a cosmological constant.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.