Quantum Field Theory and Cosmology

该奖项支持量子场论和宇宙学之间相互作用的研究。量子力学的一个中心预言是，每一个自由度都有一个不可约的最小运动量。在一般条件下，量子涨落在空间的随机位置出现，持续很短的时间，然后随着新的涨落在其他位置出现而消失。然而，宇宙学的一个核心预测是，非常早期的宇宙经历了一个被称为“原始膨胀”的加速膨胀阶段。在原始暴胀期间出现的引力场的量子涨落会无限期地持续下去，随着新的涨落的出现，它们的强度也会增强。这些波动改变了粒子的传播方式，力对空间和时间的依赖，甚至改变了宇宙膨胀的速度。虽然精确的计算是不可能的，但逐次逼近的标准方法表明，这些效应随着时间的推移而增长，在力定律的情况下，随着分离而增长，直到它们变得如此强大，以至于标准计算技术失效。一些研究人员怀疑这个结论的真实性，因为引力场在不同的坐标系下会给出不同的结果，比如黑洞视界上著名的史瓦西奇点，它实际上是糟糕坐标的产物。确定暴胀产生的量子涨落的影响是真实存在的，并设计出一种将其外推到这些涨落较强的状态的程序，有可能彻底改变基础理论。特别是，这个项目将确定是否一些古怪的参数（例如，小于正常物质组成的当前能量密度的5%）似乎描述了我们当前的宇宙，可以用量子效应来解释，量子效应在原始膨胀阶段变得强大。该项目还将促进教学、培训和学习。虽然PI现在和过去的研究生都是根据证明的能力选择的，但值得注意的是，其中一半是女性或西班牙裔。在这个项目的过程中，PI和他的研究生将与苗顺培教授（台湾），Tomislav Prokopec教授（荷兰）和Nikolaos Tsamis教授（希腊）合作(1)证明引力波动的影响不是坐标伪像；(2)开发一种技术，将它们外推到它们变得强大的政权；(3)利用Donoghue意义上的低能量有效场论对这些现象进行建模；(4)研究其他领域的可比效应。虽然会有一些数值工作，但大多数分析将是解析的，并将采用Schwinger-Keldysh形式主义，重整化群，Starobinsky的随机形式主义和宇宙摄动理论。在当前这个时代，确定来自原始暴胀的量子引力涨落会产生可测量的效应，将彻底改变基础理论。除此之外，这有可能解释什么导致了原始膨胀，为什么现在的宇宙正在加速膨胀，为什么米尔格罗姆的修正牛顿动力学（MOND）对星系结构给出了如此准确的描述。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。

This award supports work at the interplay between quantum field theory and cosmology. A central prediction of quantum mechanics is that every degree of freedom has an irreducible minimum amount of motion. Under ordinary conditions quantum fluctuations emerge at random locations in space, persist for a brief time, and then disappear as new fluctuations emerge at other locations. However, a central prediction of cosmology is that the very early universe underwent a phase of accelerated expansion known as "primordial inflation". Quantum fluctuations of gravitational fields which emerge during primordial inflation persist indefinitely, and their strength builds up as new fluctuations emerge. These fluctuations change how particles propagate, how forces depend on space and time, and even how fast the universe expands. Although exact computations are not possible, the standard method of successive approximations shows that these effects grow with time, and with separation in the case of force laws, until they become so strong that standard computational techniques break down. Some researchers doubt the reality of this conclusion because gravitational fields can give different results in different coordinate systems, like the famous Schwarzschild singularity at the event horizon of a black hole, which is really an artifact of bad coordinates. Establishing that the effects of quantum fluctuations from inflation are real, and devising a procedure for extrapolating them to regimes in which they are strong, has the potential to revolutionize fundamental theory. In particular, this project will establish whether or not some of the outlandish parameters (e.g., less than 5% of the current energy density composed of normal matter) that seem to describe our current universe can be explained by quantum effects which became strong during the phase of primordial inflation. This project will also promote teaching, training and learning. Although the PI's current and past graduate students were selected for proven ability, it is worth noting that half of them are either female or Hispanic. During the course of this project the PI and his graduate students will collaborate with Professors Shun-Pei Miao (Taiwan), Tomislav Prokopec (Holland) and Nikolaos Tsamis (Greece) on (1) demonstrating that the effects of gravitational fluctuations are not coordinate artifacts; (2) developing a technique for extrapolating them to regimes where they become strong; (3) modeling these phenomena using low energy effective field theory in the sense of Donoghue; and (4) studying comparable effects from other fields. Although there will be some numerical work, most of the analysis will be analytic and will employ the Schwinger-Keldysh formalism, the renormalization group, Starobinsky's stochastic formalism and cosmological perturbation theory. Establishing that quantum gravitational fluctuations from primordial inflation induce measurable effects during the current epoch would revolutionize fundamental theory. Among other things, this has the potential to explain what caused primordial inflation, why the current universe is undergoing accelerated expansion and why Milgrom's MOdified Newtonian Dynamics (MOND) gives such an accurate description of galactic structure.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.