Understanding Quantum Gravity from Very Early Universe

尽管在过去的一个世纪里做出了巨大的努力，量子引力理论仍然难以捉摸。需要量子引力不仅是因为概念上的原因，而且也是为了理解物理学中的基本问题，比如大爆炸和黑洞奇点。已经提出了各种各样的候选人，这项拨款支持的研究专门用于圈量子引力。当将其应用于宇宙学——环量子宇宙学时，一幅普朗克尺度物理学的连贯图景就出现了：大爆炸奇点被量子弹跳所取代，这纯粹是由于量子几何效应。本研究系统地研究了这一问题和相关问题，并将研究具有挑战性的物理问题与先进的数学方法结合起来，这将为物理学和应用数学的几个不同领域的学生和合作者提供出色的机会。所要发展的理论、技术和方法不仅将用于上述领域，而且将用于更广泛的物理和应用数学的基础问题。将特别关注在STEM领域和工程领域招募和吸引代表性不足的群体的学生。尽管环量子宇宙学（LQC）取得了各种成功，但一个重要的问题是它与环量子引力（LQG）的联系。LQC的出发点是首先通过施加同质性对哈密顿量进行约简，然后利用LQG技术对经典约简哈密顿量进行量化。然而，在LQG中，对称约简和量子化的过程通常不会交换，理解LQC捕获完整LQG的物理特性有多好是很重要的。在过去的几年里，修正环量子宇宙学得到了深入的研究，目前取得的进展非常令人鼓舞，但由于宇宙在弹跳前阶段的演化发生了巨大变化，几个基本问题仍然存在。本奖项的研究将致力于系统地研究：(i)从环量子引力的完整理论出发的量子宇宙学摄动和初始条件；（ii）非均质性、各向异性和非高斯性的演变；（三）对近期宇宙学观测中发现的异常现象的解析，以及当前和未来观测中圈量子引力的观测信号。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。

A theory of quantum gravity still remains elusive, despite enormous efforts in the past century. Quantum gravity is needed not only for conceptual reasons but also for the understanding of fundamental issues in physics, such as the big bang and black hole singularities. Various candidates have been proposed, and the research supported by this grant is devoted to loop quantum gravity. When applying it to cosmology - the loop quantum cosmology, a coherent picture of Planck scale physics has emerged: the big bang singularity is replaced by a quantum bounce, purely due to quantum geometric effects. This research investigates systematically this and related issues and shall combine studies in challenging physics problems with advanced mathematical methods, which will provide outstanding opportunities for students and collaborators across several different areas of physics and applied mathematics. The theory, techniques and methods to be developed will be used not only in the aforementioned fields, but also in a wider range of fundamental issues in physics and applied mathematics. Particular attention will be put to recruit and attract students from under-represented groups in STEM fields and engineering.Despite the various successes of Loop Quantum Cosmology (LQC), an important issue is its connection to loop quantum gravity (LQG). The starting point of LQC is first to reduce the Hamiltonian by imposing homogeneity and then to quantize the classically reduced Hamiltonian by using the techniques of LQG. However, in LQG the processes of symmetry reduction and quantization do not commute in general, and it is important to understand how well the physics of the full LQG is captured by LQC. In the past couple of years, modified loop quantum cosmologies have been intensively studied, and the progress made so far is very encouraging, but several fundamental questions still remain, due to the dramatic change of the evolution of the universe in the pre-bounce phase. The research of this award will be devoted to investigating systematically: (i) quantum cosmological perturbations and initial conditions from the full theory of loop quantum gravity; (ii) the evolutions of inhomogeneities, anisotropies and non-Gaussianities; and (iii) resolutions of anomalies found in recent cosmological observations, and observational signals of loop quantum gravity for current and forthcoming observations.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.