The Cosmological Bootstrap

该项目旨在开发新的数学技术，使我们能够更有效地计算宇宙相关器，这是早期宇宙宇宙学中的基本可观测物，并为我们提供对其基本结构的更好理解。该项目旨在推导出原始非高斯性的分类，这是当前和即将进行的大量宇宙微波背景和大尺度结构调查的主要探测目标之一。这种基于对称性和场内容的分类，将使我们能够在检测到非高斯的情况下，直接了解早期宇宙宇宙学的理论。分类将集中在引力子和曲率微扰之间的所有三点函数。这些三点函数将使用对称性、局部性和统一性的组合来引导，并要求它们一起形成一致的四点函数。该项目还将致力于推导递归关系，从递归关系中可以从较低的点计算出较高的宇宙学相关函数。重点将放在标量有效场理论和无质量自旋场理论，如杨-米尔斯和重力。对于具有非线性实现对称性的标量有效场理论，我们期望存在这样的递推关系，而对于无质量自旋场理论，规范不变性表明存在这样的关系。指导将来自平面空间中散射振幅的递归关系，因为这些振幅包含在它们的宇宙对应物中。领导这些项目的学生将在理论宇宙学中最令人兴奋和发展最快的领域之一工作。学生还将受益于一个非常活跃的英国和国际社会的研究人员在这个领域的工作，现在坐在理论宇宙学的最前沿。

This project will aim to develop new mathematical techniques that will enable us to more efficiently compute cosmological correlators, which are the fundamental observables in early universe cosmology, and provide us with a better understanding of their fundamental structures.The project will aim to derive a classification of primordial non-Gaussianities which are one of the primary detection goals of the large number of current and upcoming Cosmic Microwave Background and Large-Scale Structure surveys. Such a classification, which will be based on symmetries and field content, will enable us to straightforwardly learn about theories of early universe cosmology given a detection of non-Gaussianities. The classification will focus on all three-point functions between gravitons and curvature perturbations. These three-point functions will be bootstrapped using a combination of symmetries, locality and unitarity and by demanding that together they form consistent four-point functions.The project will also aim to derive recursion relations from which higher-point cosmological correlation functions can be computed from lower points ones. The focus will be on both scalar effective field theories, and theories of massless spinning fields such as Yang-Mills and gravity. For scalar effective field theories with non-linearly realised symmetries we expect such recursion relations to exist, while for theories of massless spinning fields gauge invariance suggests the existence of such relations. Guidance will come from recursion relations for scattering amplitudes in flat-space, given that these amplitudes are contained within their cosmological counterparts.The student leading these projects will be working within one of the most exciting and fastest growing areas of theoretical cosmology. The student will also benefit from a very lively UK and international community of researchers working in this field which now sits at the forefront of theoretical cosmology.