Explorations in Quantum Gravity: Cosmological and Black Hole Spacetimes

爱因斯坦的广义相对论虽然在描述宇宙演化和黑洞动力学方面取得了巨大的成功，但在大爆炸和黑洞内部等奇点上失败了。人们普遍认为，克服奇点问题的量子引力理论将给出爱因斯坦理论中长期存在的问题的答案，例如大爆炸之外是否存在空间和时间，用什么来取代大爆炸和黑洞奇点，爱因斯坦理论之外的物理学是什么，以及它如何留下观测特征。这项由美国国家科学基金会资助的研究旨在利用环路量子引力技术解决各种这样的基本问题。这项研究的一个主要目标是发现普朗克尺度的新物理，它负责通过结合使用各种量子引力宇宙学和黑洞时空的严格分析、唯象和最先进的数值方法来解决宇宙微波背景中的奇点和稳健的观测特征。这一研究领域的进展将使从事经典和量子引力和宇宙学的社区和科学家受益，并可能导致公众感兴趣的基本问题的答案。研究生和博士后研究人员将接受关于量子引力最先进研究的培训。这项研究的主要目标是发现从时空的量子性质中涌现出来的新物理，并将取代大爆炸奇异性的量子弹跳的结果推广到各向异性和非均匀的时空。利用循环量子引力技术，它旨在解决基本问题，如量子重力中奇点的命运，量子重力影响非常早期宇宙和黑洞物理的方式，以及在宇宙微波背景下量子重力的可靠潜在观测特征。这些基本问题将通过：(I)系统地研究不同时空的量子化和由此产生的物理，包括各向异性、不均匀和黑洞，(Ii)通过分析对宇宙学微扰的影响来探索量子引力的现象学含义，以及(Iii)解决量子宇宙学的基本问题，如量子到经典的跃迁和量子概率。这项研究有望大大拓宽和推进我们对量子引力物理学的理解，并导致对时空本质的洞察，超越爱因斯坦的广义相对论。这一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。

Einstein’s theory of general relativity, though immensely successful in describing the evolution of the universe and the dynamics of black holes, breaks down at singularities such as the big bang and inside the black holes. It has been widely believed that a quantum theory of gravity overcoming the problems of singularities would give answers to long-standing questions in Einstein’s theory, such as if there is space and time beyond the big bang, what replaces big bang and black hole singularities, what is the physics beyond Einstein’s theory and how does it leave observational signatures. This NSF funded research aims to address various such fundamental questions using techniques of loop quantum gravity. A primary objective of this research would be to discover new physics at the Planck scale which is responsible for the resolution of singularities and robust observational signatures in the cosmic microwave background by using a combination of rigorous analytical, phenomenological and state-of-the-art numerical methods for various quantum gravitational cosmological and black hole spacetimes. Progress in this area of research will benefit communities and scientists engaged in classical and quantum gravity and cosmology and may lead to answers to fundamental questions which are of interest to the public. Graduate students and postdoctoral researchers will be trained on state-of-the-art research on quantum gravity. The primary goal of this research is to discover the new physics emerging from the quantum properties of spacetime and generalize the results on quantum bounce, which replaces the big bang singularity, to anisotropic and inhomogeneous spacetimes. Using techniques of loop quantum gravity it aims to address fundamental issues such as the fate of singularities in quantum gravity, the way quantum gravity affects the physics of the very early universe and black holes, and reliable potential observational signatures of quantum gravity in the cosmic microwave background. These fundamental questions will be explored by: (i) systematically investigating the quantization and resulting physics of different spacetimes including anisotropies, inhomogeneities and black holes, (ii) exploring phenomenological implications of quantum gravity by analyzing effects on cosmological perturbations and (iii) addressing foundational issues in quantum cosmology such as the quantum to classical transition and quantum probabilities. This research is expected to significantly broaden and advance our understanding of the physics of quantum gravity and lead to insights on the nature of spacetime beyond Einstein’s theory of general relativity.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.