Effective Descriptions of Quantum Gravity and Cosmology

广义相对论和量子力学是支配基本物理、时空和基本粒子的两大理论。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。这个项目研究了广义相对论和量子力学都相关的广泛的系统。主要感兴趣的方法是允许人们通过近似推导物理含义，并使用结果来指导量子引力的发展。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。相关方法也可以用在不涉及广义相对论的系统中，在这些系统中，它们可以帮助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。本项目的目标是引入和评估基于正则量子化的系统分析一套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者进行比较，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。

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 project investigates a wide range of systems in which both general relativity and quantum mechanics are relevant. The main interest is given by methods that allow one to derive physical implications by approximations, and to use the results to guide the developments 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.The objective of this project 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.