Amplitudes meet Cosmology: A (Scalar) Primer

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.

137 pages, figures with TikZ, invited review

References in corpus (25)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• The Effective Field Theory of Inflation
• Classical Polylogarithms for Amplitudes and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• De Sitter Space and Eternity
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• The IR stability of de Sitter: Loop corrections to scalar propagators
• Semiclassical relations and IR effects in de Sitter and slow-roll space-times
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Conformal Symmetries of Adiabatic Modes in Cosmology
• Breakdown of Semiclassical Methods in de Sitter Space
• Taming Tree Amplitudes In General Relativity
• On the proper treatment of massless fields in Euclidean de Sitter space
• Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation
• On-shell constructibility of tree amplitudes in general field theories
• Loops and trees
• Characters of different secular effects in various patches of de Sitter space
• Stochastic Inflation at NNLO
• Resonant Trispectrum and a Dozen More Primordial N-point functions
• Nonperturbative Negative Geometries: Amplitudes at Strong Coupling and the Amplituhedron
• Solid Consistency
• Solid Soft Theorems
• Positive Geometries and Differential Forms with Non-Logarithmic Singularities I
• On the consistency of (partially-)massless matter couplings in de Sitter space

Cited by in corpus (16)

• The graviton four-point function in de Sitter space
• The Open Effective Field Theory of Inflation
• Cosmological Correlators Through the Looking Glass: Reality, Parity, and Factorisation
• Probing the initial state of inflation: analytical structure of cosmological correlators
• The Geometry of Cosmological Correlators
• de Sitter at all loops: the story of the Schwinger model
• Rational Wavefunctions in de Sitter Spacetime
• Cosmological cutting rules for Bogoliubov initial states
• Internal boundaries of the loop amplituhedron
• The Massive Flat Space Limit of Cosmological Correlators
• Cosmohedra
• The Asymptotic Structure of Cosmological Integrals
• Differential equations for tree--level cosmological correlators with massive states
• Cosmological Infrared Subtractions & Infrared-Safe Computables
• Correlator Polytopes
• A Match Made in Heaven: Linking Observables in Inflationary Cosmology