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Amplitudes meet Cosmology: A (Scalar) Primer
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Amplitudes meet Cosmology: A (Scalar) Primer
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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.
Forward citations
Cited by 10 Pith papers
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All Tree-Level Massive Cosmological Correlators via Spectral Gluing
Tree-level massive de Sitter correlators are constructed by gluing Lauricella-type vertex functions according to graph combinatorics, and the hypergeometric content collapses to rational functions once the dynamical p...
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Cosmological Weight-Shifting Matrices
Introduces weight-shifting matrices for de Sitter diagrams, generalized with Kronecker products to arbitrary tree-level graphs, to derive massless wavefunction coefficients from conformally coupled seeds.
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De Sitter correlators in conformally coupled φ³ theory admit a time-integral representation built from flat-space correlators, revealing intrinsic simplifications including vanishing of odd conjugate-momentum graphs a...
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Differential Equations for Massive Correlators
A graph-tubing combinatorial framework governs the first-order differential equations obeyed by master integrals for massive cosmological correlators in de Sitter space.
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de Sitter Wavefunction from Quadrangular Polylogarithms: Chain Graphs
The n-site chain graph contribution to the de Sitter cosmological wavefunction in conformally coupled φ³ theory is expressed explicitly in terms of Rudenko's quadrangular polylogarithms.
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Picard-Fuchs Equations of Twisted Differential forms associated to Feynman Integrals
An extension of the Griffiths-Dwork algorithm produces twisted Picard-Fuchs operators for hypergeometric, elliptic, and Calabi-Yau motives from families of Feynman integrals.
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Correlators are simpler than wavefunctions
Equal-time correlators are simpler than wavefunctions because they come from full-spacetime integrals; this implies fewer poles, cleaner factorization, and a systematic pole expansion whose first subleading term vanishes.
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Correlators are simpler than wavefunctions
Equal-time correlators are simpler than wavefunctions because full-spacetime integration of propagators eliminates certain poles and yields a vanishing first subleading term in every Laurent expansion around poles.
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A Match Made in Heaven: Linking Observables in Inflationary Cosmology
In dynamical Chern-Simons inflation the parity-odd trispectrum is a double copy of the mixed bispectrum and parity-odd power spectrum via a prior factorization formula.
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De Sitter Representations
Review of so(1,D) representations for de Sitter space across all D, covering mixed symmetry and fermions, connected to propagating fields.
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