The analytic cosmological correlator

该项目的目标是预测在大爆炸的最初几分之一秒的宇宙膨胀过程中产生的宇宙相关物。宇宙学相关器为我们宇宙中所有成分的后续演化提供了初始条件，例如光子、中微子、重子物质和暗物质。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中进行测试（例如星系和弱透镜调查，强度测绘等）。到目前为止，只检测到两点相关函数，国际上大量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，该方法与模型无关，并依赖于物理基本原理的强加约束。具体来说，相关的原则是对称性、概率守恒（统一性）、远距离作用的不存在（局部性）和因果关系的一致分离（因果性）。近年来，概率守恒所施加的限制已经得到了更好的理解，但仍需要进一步的进展。这个项目的一个目标是在不依赖摄动理论的情况下表述这些统一约束。这对于从可能的紫外线完井中提取信息至关重要，因为这些信息通常是未知的。局部性所施加的约束，即在距离上不存在相互作用，将以复杂运动学相关器增长的精确界限的形式导出。我们的目标是在大的理论类别中建立这些边界，例如在近似德西特时空中具有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相关器的分析结构，其方式类似于平坦时空中散射振幅的情况。迄今为止还不知道有这样的限制。最后，在这个博士项目的最后一部分，上述成分将结合起来，得出低能有效场论必须满足的边界，如果他们承认一致的，统一的，局部的和因果的uv补全。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）推导。

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).