Dynamics and Symmetry in Quantum Gravity

基础物理学面临的一个重要问题是，爱因斯坦的引力理论和量子力学中久经考验的定律如何一致--量子引力的问题。这个问题对于理解我们宇宙的起源--大爆炸--以及理解黑洞的最终命运是至关重要的。该奖项旨在弥合环路量子引力(LQG)的完整理论与基于LQG的宇宙学和黑洞简化模型之间的差距，这些模型最近在做出潜在的观测预测方面取得了成功。这样的桥梁将允许未来将此类模型与数据进行比较，以告诉我们有关量子引力基本定律的确切细节。通过让研究生参与前沿物理，并与其他研究小组互动，该奖项将对未来科学家的发展产生广泛和长期的影响。研究结果将通过同行评议的出版物和科学讲座向科学界传播，并通过公开讲座和其他方式向公众传播。对于宇宙学和黑洞，LQG中不同的动力学方案的观测结果将被确定。要做到这一点，PI将首先找到从简化的量子宇宙学模型-环路量子宇宙学(LQC)-到满足PI小组最近建立的微分同态不变量、齐性和各向同性的量子判据的微分同胚不变LQG态中的态的嵌入。这种嵌入将使LQG中关于动力学的不同建议被转换为LQC，从而使用已建立的方法区分它们的观测结果。通过PI群最近证明的对结果可能性的严格限制，找到相应的LQC动力学的任务被简化。对黑洞也将采取类似的策略。PI还计划进一步开发LQG的历史总和方法，即所谓的自旋泡沫。在PI以前的工作中，对流行的EPRL自旋泡沫模型进行了修改，以纠正其半经典限制，产生了“适当的自旋泡沫模型”。将开发有效的数值方法来使用该模型进行计算。将探索解决旋转泡沫中长期存在的问题的可能性。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

An important question facing fundamental physics is how the well-tested laws of Einstein's theory of gravity and quantum mechanics are consistent - the question of quantum gravity. This question is central for understanding the very origin of our universe, the big bang, as well as for understanding the final fate of black holes. The award seeks to bridge the gap between the full theory of loop quantum gravity (LQG) and simplified models of cosmology and black holes based on LQG that have been recently successful in making potential observational predictions. Such a bridge would allow future comparisons of such models with data to tell us exact details about the fundamental laws of quantum gravity. By enabling graduate students to participate in frontier physics, and to interact with other research groups, this award will have a broad and long-term impact on the development of future scientists. The results of the research will be disseminated to the scientific community through peer reviewed publication and scientific lectures, as well as to the general public through public lectures and other means. The observational consequences, for both cosmology and black holes, of different proposals for dynamics in LQG will be determined. To accomplish this, the PI will first find an embedding of states from the simplified quantum cosmological model - Loop Quantum Cosmology (LQC) - into diffeomorphism invariant LQG states that satisfy the diffeomorphism invariant, quantum criterion for homogeneity and isotropy recently established by the PI’s group. This embedding will enable different proposals for dynamics in LQG to be translated into LQC, and thereby to distinguish their observational consequences using established methods. The task of finding the corresponding LQC dynamics is simplified by the severe restriction on the resulting possibilities proven recently by the PI’s group from diffeomorphism invariance. An analogous strategy will be carried out for black holes. The PI additionally plans to further develop the sum over histories approach to LQG, known as spin-foams. In prior work of the PI, the prevailing EPRL model of spin-foams was modified to correct its semiclassical limit, yielding the `proper spin-foam model’. Efficient numerical methods will be developed to perform calculations using this model. Possibilities for solving long-standing issues in spin-foams will be explored.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.