The analytic cosmological correlator

解析宇宙相关器

• 批准号: 2750670
• 金额: --
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2750670
• 关键词: analytic; cosmological; correlator

The goal of the project is to make predictions for cosmological correlators generated during cosmic inflation in the first fraction of a second of the big bang. Cosmological correlators provide the initial conditions for the subsequent evolution of all constituents of our universe, including for example photons, neutrinos, baryonic matter and dark matter. Hence, these predictions can be tested in current and upcoming cosmological surveys of the cosmic microwave background and large scale structures (e.g. galaxy and weak-lensing surveys, intensity mapping, etc). So far only the two point correlation function has been detected and one of the main science goals of a large number of international experiments is to detect higher point functions, collectively denoted as non-Gaussianity.This project aims at developing a new methodology to compute non-Gaussianity that is model-agnostic and relies on imposing constraints from fundamental principles of physics. In particular, the relevant principles are symmetries, the conservation of probability (unitarity), the absence of action at distance (locality) and the consistent separation between cause and effect (causality). The constraints imposed by the conservation of probability have been much better understood in recent years, but further progress is still required. One goal of this project is to formulate these unitarity constraints without relying on perturbation theory. This will be essential to extract information from possible UV-completions, which are usually not known in detail.The constraints imposed by locality, namely the absence of interaction at distance, will be derived in the form of precise bounds on the growth of correlators for complex kinematics. The goal is to establish these bounds in full generality for large classes of theories, e.g. for particles of any mass and any spin on an approximately de Sitter spacetime. The constraints from causality will dictate the analytic structure of correlators for complex kinematics, in a way similar to what happens for scattering amplitudes in flat spacetime. No such constraints are known to date.Finally, in the last part of this PhD project, the above ingredients will be combined to derive bounds that low-energy effective field theory have to satisfy if they are to admit a consistent, unitarity, local and causal UV-completions. These so-called positivity bounds are known in flat space but not in cosmological spacetime. Here they will be derived around an inflationary spacetime and for a dark energy dominated universe (quasi de Sitter).

该项目的目标是对大爆炸第一秒的宇宙膨胀过程中产生的宇宙相关器进行预测。宇宙学相关器为宇宙所有成分（包括光子、中微子、重子物质和暗物质）的后续演化提供了初始条件。因此，这些预测可以在当前和即将进行的宇宙微波背景和大尺度结构的宇宙学调查（例如星系和弱透镜调查、强度测绘等）中得到检验。到目前为止，仅检测到了两点相关函数，大量国际实验的主要科学目标之一是检测更高的点函数，统称为非高斯性。该项目旨在开发一种计算非高斯性的新方法。 -与模型无关的高斯性，依赖于物理基本原理的约束。具体而言，相关原则包括对称性、概率守恒（幺正性）、远距离作用的缺失（局域性）以及因果关系的一致分离（因果性）。近年来，人们对概率守恒所施加的限制有了更好的理解，但仍需要进一步的进展。该项目的目标之一是在不依赖微扰理论的情况下制定这些幺正性约束。这对于从可能的 UV 完井中提取信息至关重要，而 UV 完井通常无法详细了解。局域性所施加的约束，即远距离相互作用的缺乏，将以相关器增长的精确界限的形式导出：复杂的运动学。目标是为大类理论建立完全通用的界限，例如对于近似德西特时空上任意质量和任意自旋的粒子。因果关系的约束将决定复杂运动学的相关器的分析结构，其方式类似于平坦时空中的散射振幅所发生的情况。迄今为止，尚不存在这样的约束。最后，在本博士项目的最后一部分，将结合上述成分来推导出低能有效场论必须满足的界限，如果它们要承认一致的、幺正的、局部的和因果 UV 完成。这些所谓的正边界在平坦空间中是已知的，但在宇宙时空中是未知的。在这里，它们将围绕暴胀时空和暗能量主导的宇宙（准德西特）导出。