标题： S矩阵马拉松记录：膨胀宇宙中的可观测量 显示英文标题

标题： Records from the S-Matrix Marathon: Observables in Expanding Universes

摘要： 在膨胀宇宙中的可观测量对于理解早期宇宙的物理至关重要。 在这些讲座中，我们回顾了最近在理解其数学结构方面的进展，并提取了其中编码的物理内容。 在讨论了膨胀背景最显著的特征及其对定义可观测量的影响之后，我们重点研究了所谓的 Bunch--Davies波函数。 我们从一般角度分析了它的解析性质，并在微扰理论中为一类特殊的标量玩具模型引入了它的积分表示。 我们讨论了与通常的费曼规则和图上的组合规则相关的图示法，这些规则生成了一个没有虚假极点的表示。 这种组合规则起源于宇宙多面体的组合学，我们对其定义和主要特征提供了温和的介绍。 最后，宇宙多面体的组合学被证明决定了编码宇宙积分渐近行为的一类特殊嵌套多面体的组合学。 我们提供了此类结构和行为的一般描述，这对于理解在膨胀背景中困扰可观测量的红外发散具有关键重要性。 这些笔记基于2024年3月11日至22日在高级研究所举行的S-Matrix马拉松研讨会期间举行的一系列讲座。 显示英文摘要

摘要： Observables in expanding universes are crucial to understand the physics of the early universe. In these lectures, we review some recent progress in understanding their mathematical structure and extract the physics encoded in them. After discussing the most salient features of an expanding background and their consequences for defining an observable, we focus on the so-called Bunch--Davies wavefunctional. We analyze its analytic properties on general grounds and introduce an integral representation for it in perturbation theory for a special class of scalar toy models. We discuss both the diagrammatics associated to the usual Feynman rules and combinatorial rules on the graphs, which generate a representation free of spurious poles. Such combinatorial rules find their origin in the combinatorics of the cosmological polytopes of which we provide a gentle introduction to its definition and its main features. Finally, the combinatorics of the cosmological polytopes turns out to determine the combinatorics of a special class of nestohedra that encode the asymptotic behaviour of the cosmological integrals. We provide a general description of such structures and behaviour, which is of crucial importance to understand the infrared divergences which plague observables in an expanding background. These notes are based on a series of lectures held during the S-Matrix Marathon workshop at the Institute for Advanced Study on 11--22 March 2024.