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工作。量子力学的一个中心预言是，每个自由度都有一个不可约的最小运动量。在普通条件下，量子涨落出现在空间中的随机位置，持续很短的时间，然后随着新的涨落出现在其他位置而消失。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。在原初暴胀期间出现的引力场的量子涨落会无限期地持续下去，并且随着新的涨落的出现，它们的强度会不断增强。这些波动改变了粒子的传播方式，力如何依赖于空间和时间，甚至宇宙膨胀的速度。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，这些效应随着分离而增长，直到它们变得如此强大，以至于标准计算技术崩溃。一些研究人员怀疑这一结论的真实性，因为引力场在不同的坐标系中会给出不同的结果，就像黑洞事件视界处著名的史瓦西奇点，这实际上是坏坐标的产物。确认暴胀产生的量子涨落效应是真实的，并设计出一种程序，将它们外推到它们很强的区域，有可能彻底改变基础理论。特别是，该项目将确定是否有一些古怪的参数（例如，不到5%的当前能量密度组成的正常物质），似乎描述了我们目前的宇宙可以解释的量子效应，成为强大的原始膨胀阶段。该项目还将促进教学、培训和学习。虽然PI的现任和过去的研究生被选为证明能力，值得注意的是，他们中的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 Proklav（荷兰）和Nikolaos Tsamis（希腊）合作（1）证明引力波动的影响不是坐标伪影;（2）开发一种将它们外推到它们变得强大的区域的技术;（3）用Donoghue意义下的低能有效场理论模拟这些现象;（4）研究其他场的可比效应。虽然会有一些数值计算工作，但大部分的分析将是解析的，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学微扰理论。在当前的时代，建立由原初暴胀引起的量子引力涨落会引起可测量的效应，这将彻底改变基础理论。除此之外，这有可能解释是什么导致了原始膨胀，为什么现在的宇宙正在经历加速膨胀，为什么米尔格罗姆的修改后的牛顿动力学（MOND）对银河系结构给出了如此准确的描述。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

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.