Amplitudes meet Cosmology: A (Scalar) Primer

TL;DR

This paper reviews recent advances in understanding quantum observables in cosmology, emphasizing boundary-based approaches, their analytic structures, and connections to fundamental principles, inspired by scattering amplitude techniques.

Contribution

It introduces a boundary-centric framework for cosmological observables, linking their structure to on-shell amplitude methods and geometric representations like cosmological polytopes.

Findings

Boundary approach clarifies the structure of the wavefunction of the universe.

Cosmological polytopes provide a geometric understanding of cosmological processes.

Analytic properties of quantum observables reveal deep connections to fundamental principles.

Abstract

We review the most recent progress in our understanding of quantum mechanical observables in cosmology in the perturbative regime. It relies on an approach that considers them directly as functions of the data at the space-like boundary at future infinity prescinding from the explicit time evolution. It takes inspiration from the on-shell formulation of perturbative scattering amplitudes developed in the past 20 years: starting with the requirement of consistency with some fundamental principles such as causality, unitarity and locality, it provides different ways of phrasing and extracting predictions. In this review, we aim to provide a pedagogical treatment of the most recent insights about the analytic structure of the perturbative quantum mechanical observables in cosmology, its relation to fundamental principles as well as physical processes, and how such observables and their features emerge from novel well-defined mathematical objects with their own first principle definition. The review is divided in three parts: Part 0 discusses the definition of quantum mechanical observables in cosmology and some general principles; Part I reviews the boundary approach to the analysis and computation of the perturbative wavefunction of the universe; Part II provides an introduction to the combinatorial-geometrical description of cosmological processes in terms of cosmological polytopes.