Effective Descriptions of Quantum Gravity and Cosmology

广义相对论和量子力学是支配时空和基本粒子基本物理的两大理论。然而，目前还不知道如何将它们结合在一起，形成一个一致的量子引力理论。因此，令人着迷的现象，如大爆炸的最初阶段或黑洞的核心，仍然不在我们目前的理解范围之内。这项研究调查了广义相对论和量子力学都相关的广泛的系统，从而促进了科学的进步。主要关注的是允许人们通过适当的近似推导物理含义，并使用结果来指导量子引力发展的方法。对大爆炸和黑洞的应用往往会得出能引起公众兴趣的结论。相关方法也可以用于不涉及广义相对论的系统，在这些系统中，它们可能有助于解决技术问题或以一种新的方式交流结果，例如支持量子力学的教学。这项研究通过将未被充分代表的群体的成员纳入科学领域来支持多样性。本研究的目的是引入和评估基于正则量子化的系统分析一组候选量子引力理论的物理含义的新方法。在整个物理学中，通过对经典方程进行量子修正的有效理论，提供了一个强大的工具来推导潜在的可观测现象。与量子态方程相比，这样的系统可以更容易地进行分析或数值评估，因此是发现新现象的更直接来源。虽然推导有效方程的标准技术不适用于正则量子引力，但存在适用于正则量子理论的一般方案(由PI引入)，并在该项目中用于解决量子重力的主要问题。它为在量子引力的广泛背景下评估物理现象的长期计划提供了基础。这种系统的推导将使以前在简化模型中发现的效应有可能建立在坚实的基础上，发现新的现象并提供可靠的预测。结果将被用来将该理论与量子引力的其他候选人进行比较，并有可能在两种方法之间进行卓有成效的思想和技术转移。这一奖项反映了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。

General relativity and quantum mechanics are the two major theories that govern fundamental physics of space-time and of elementary particles. However, it is not known how they could be combined to a consistent theory of quantum gravity. Fascinating phenomena such as the very first stages of the Big Bang or the cores of black holes therefore remain out of the reach of our current understanding. This research investigates a wide range of systems in which both general relativity and quantum mechanics are relevant, thereby promoting the progress of science. The main focus is on methods that allow one to derive physical implications by suitable approximations, and to use the results to guide the development of quantum gravity. Applications to the Big Bang and black holes often lead to conclusions that capture the interest of the general public. Related methods can also be used in systems not involving general relativity, where they may help to solve technical questions or to communicate results in a new way, supporting for instance the teaching of quantum mechanics. This research supports diversity by including members of under-represented groups in science.The objective of this research is to introduce and evaluate new methods for a systematic analysis of physical implications of one set of candidate theories of quantum gravity, based on canonical quantization. Throughout physics, a powerful tool to derive potentially observable phenomena is given by effective theories which provide quantum corrections to the classical equations. Such systems can more easily be evaluated, analytically or numerically, than equations for quantum states and thus are more direct sources for the discovery of new phenomena. While standard techniques to derive effective equations do not apply to canonical quantum gravity, a general scheme applicable to canonical quantum theories exists (introduced by the PI) and is used in this project to address the main problems of quantum gravity. It provides the basis for a long-term program evaluating physical phenomena in the broad context of quantum gravity. Such a systematic derivation will make it possible to put effects found previously in simplified models on a firm footing, uncover new phenomena and provide reliable predictions. Results will be used to compare the theory with other candidates of quantum gravity, with the potential of a fruitful transfer of ideas and techniques between the approaches.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.