The analytic cosmological correlator

该项目的目标是预测宇宙膨胀过程中产生的宇宙膨胀子，在大爆炸的第一个瞬间。宇宙学的量子化为我们宇宙的所有组成部分，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到来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，强度映射等）中进行测试。迄今为止，只有两点相关函数被检测到，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。本项目旨在开发一种新的方法来计算非高斯性，该方法与模型无关，并依赖于物理学基本原理的约束。特别是，相关的原则是对称性、概率守恒（么正性）、远距离作用的不存在（局部性）以及因果关系之间的一致分离（因果关系）。近年来，人们对概率守恒所施加的限制有了更好的理解，但仍需取得进一步的进展。这个项目的一个目标是制定这些不依赖于微扰理论的么正性约束。这将是必不可少的，以提取信息，从可能的UV-完成，这通常是不知道的细节。由本地施加的约束，即在距离上的相互作用的情况下，将推导出的形式，精确的边界上的增长复杂的运动学。我们的目标是为大类的理论建立完全通用的这些界限，例如，对于近似德西特时空上的任何质量和任何自旋的粒子。因果关系的约束将决定复运动学中的散射子的解析结构，其方式类似于平坦时空中散射振幅的情况。最后，在本博士项目的最后一部分中，将结合上述成分，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，幺正性的，局部的和因果的UV-完成。这些所谓的正性边界在平坦空间中是已知的，但在宇宙学时空中则不然。在这里，它们将在暴胀时空和暗能量主导的宇宙（准德西特）周围导出。

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).