The Cosmological Bootstrap

这个项目的目标是开发新的数学技术，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参数，并使我们更好地了解它们的基本结构。该项目的目标是得出原始非高斯性的分类，这是目前和即将进行的大量宇宙微波背景和大规模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直接了解早期宇宙宇宙学的理论，因为它检测到了非高斯性。分类将集中在引力子和曲率扰动之间的所有三点函数。这些三点函数将使用对称性、局部性和酉性的组合进行自举，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，从低点宇宙学关联函数计算出更高点的宇宙学关联函数。重点将放在标量有效场理论和无质量旋转场理论上，如杨-米尔斯和引力。对于具有非线性实现对称性的标量有效场论，我们期望存在这样的递推关系，而对于无质量自旋场理论，规范不变性暗示了这种关系的存在。指导将来自平坦空间中散射幅度的递归关系，因为这些幅度包含在它们的宇宙学对应物中。领导这些项目的学生将在理论宇宙学最令人兴奋和发展最快的领域之一工作。这名学生还将受益于活跃的英国和国际研究人员社区，这些研究人员目前处于理论宇宙学的前沿。

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.