CAREER: Effective Descriptions of Quantum Systems in Cosmology

有效方程是从基本量子理论中提取物理现象的强大数学工具。一旦它们被派生出来，它们就会在直观的水平上显示出效果，比如在力量平衡方面。这比例如量子力学波函数的基本方程更容易可视化和计算。在一般层面和关键例子中，将在量子力学、量子宇宙学和量子引力领域系统地分析和推导新的有效方程。这些结果将被整合到本科生的量子力学和宇宙学中的量子方面的教学中，例如宇宙中结构的出现。在新的研究中，将分析量子宇宙学中大爆炸奇点的本质，提供对大爆炸时和之前宇宙状态的洞察。此外，还将研究早期宇宙中潜在的可观察到的量子引力效应和黑洞量子物理中的新现象。通过专注于效应而不是基本的数学，与其他量子引力方法的比较将成为可能。所解决的问题奠定了我们对宇宙的理解，并通常会引起广泛的兴趣。即将推出的新方法使非专业人士能够接触到量子引力的含义，并弥合了该领域基础研究和宇宙现象学之间的传统差距。通过这种方式，关键的基础设施将可供其他研究人员使用，并将产生可管理的项目，以指导学生进入该领域。通过在早期阶段将新的方法和结果融入教学，将提高对量子物理的理解。宇宙学是许多学生感兴趣的领域，现代应用的例子将提供额外的动力。具体成果将定期向研究界和公众传播。

Effective equations are a powerful mathematical tool to extract physical phenomena from fundamental quantum theories. Once they have been derived, they show effects at an intuitive level such as in the balance of forces. This is much easier to visualize and compute than the underlying fundamental equations for, e.g., a quantum mechanical wave function. At a general level as well as in key examples, new effective equations will be analyzed and derived systematically in the areas of quantum mechanics, quantum cosmology and quantum gravity. Results will be integrated in the teaching of undergraduate quantum mechanics and of quantum aspects in cosmology such as the emergence of structure in the universe. In new research, the nature of the big bang singularity in quantum cosmology will be analyzed, providing insights into the state of the universe at and before the big bang. Moreover, potentially observable effects of quantum gravity in the early universe and new phenomena in the quantum physics of black holes will be investigated. By focusing on effects rather than the underlying mathematics, comparisons with other approaches to quantum gravity will become possible.The issues addressed underlie our understanding of the universe and typically attract wide interest. New methods to be introduced make implications of quantum gravity accessible for the non-specialist and bridge the traditional gap between fundamental research in this area and cosmological phenomenology. In this way, key infrastructure will be made available to other researchers, and manageable projects to guide students to the field will be generated. By integrating new methods and results into teaching at early stages, the understanding of quantum physics will be improved. Modern examples of applications in cosmology, an area of interest to many students, will provide additional motivation. Specific results will regularly be disseminatedto the research community and the general public.