Black holes and cosmology in quantum gravity

量子引力中的黑洞和宇宙学

• 批准号: RGPIN-2017-04317
• 负责人: Husain, Viqar
• 金额: $ 2.62万
• 依托单位: University of New Brunswick
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=654138
• 关键词: Black; holes; cosmology; quantum; gravity

The physics of the small, at the scale of atomic and nuclear phenomena, is described by quantum theory. We now have broadly successful quantum theories that describe three of the four observed fundamental forces in nature: electromagnetic, weak and strong nuclear interactions. On the other hand, physics on large scales, encompassing the study of solar systems, galaxies and cosmology as a whole, is described by a gravitational theory, the most successful of which is Einstein's theory of general relativity. This theory envisions gravity as a curvature of the geometry of space and time, welded together as one entity: spacetime.*** Quantum theory is expected to be important in gravitational phenomena involving very strong gravitational fields of highly compact objects, such as black holes and the very early Universe. Combining gravitation with quantum theory is widely considered to be the frontier problem in theoretical physics, and would reveal a "quantum geometry" with matter.*** The purpose of the proposed research is to explore one approach to developing a quantum theory of gravity. This requires the use of a clock as a part of the description of geometry and matter, and helps us to clarify what is meant by "energy of the Universe." I will use this description, called the Hamiltonian theory, to study the properties of the early Universe very close to the Big Bang, and the formation of black holes, using computer simulations.*** These simulations will use a method of random sampling of the state of gravity and matter known as the Monte Carlo method. This is a very efficient and well-developed technology that has wide ranging applications, but it has so far not been applied to the study of matter and the geometry of the Universe in a fully quantum setting. This method is expected to reveal properties called phase transitions, that are familiar in solid, liquid and gas phases of matter. But if the physical system is gravity and matter, with gravity described as a spacetime curved geometry, the phases could turn out to be unusual and revealing. One interesting feature is the correlation length. This is a measure of how far apart in space physical effects are correlated. If this distance is very large, it means that very distant physical phenomena are related, or march in step. An infinite correlation length signals a phase transition.*** I expect the ideas and methods to be employed in this proposal will provide new insights into the problem of quantum gravity. These insights could guide future theoretical developments, and provide a better understanding of cosmological problems, such as dark matter and energy. The simulation methods to be used have diverse applicability, from forecasting polls to analyzing big data sets, and therefore provide important multi-disciplinary tools for training HQP. ****** ************ *** **

在原子和核现象的尺度上，微观物理学是由量子理论描述的。我们现在已经有了广泛成功的量子理论，描述了自然界中四种观察到的基本力中的三种：电磁力、弱相互作用和强相互作用。另一方面，大尺度物理学，包括对太阳系、星系和宇宙学的研究，是由引力理论描述的，其中最成功的是爱因斯坦的广义相对论。这个理论把引力想象成时空几何的曲率，焊接在一起成为一个实体：时空。 量子理论被认为在引力现象中很重要，这些引力现象涉及高度紧凑物体的非常强的引力场，例如黑洞和非常早期的宇宙。将引力与量子理论相结合被广泛认为是理论物理学的前沿问题，并将揭示物质的“量子几何”。 拟议研究的目的是探索一种发展引力量子理论的方法。这需要使用时钟作为描述几何和物质的一部分，并帮助我们澄清什么是“宇宙能量”。“我将使用这种描述，称为哈密顿理论，使用计算机模拟来研究非常接近大爆炸的早期宇宙的性质，以及黑洞的形成。 这些模拟将使用一种对重力和物质状态进行随机抽样的方法，称为蒙特卡罗方法。这是一种非常有效和发展良好的技术，具有广泛的应用，但到目前为止，它还没有被应用于在完全量子环境中研究物质和宇宙几何。这种方法有望揭示物质的固体、液体和气体相的相变特性。但是，如果物理系统是引力和物质，引力被描述为时空弯曲的几何形状，那么这些相可能是不寻常的，也是有启发性的。一个有趣的特征是相关长度。这是一个衡量空间物理效应相互关联的尺度。如果这个距离很大，这意味着很远的物理现象是相关的，或者说是同步的。无限长的相关长度表示相变。*** 我希望这个建议中所采用的思想和方法将为量子引力问题提供新的见解。这些见解可以指导未来的理论发展，并提供更好的理解宇宙学问题，如暗物质和能量。所使用的模拟方法具有不同的适用性，从预测民意调查到分析大数据集，因此为培训HQP提供了重要的多学科工具。****** ************ *** **