Analytical evaluation of cosmological correlation functions

Abstract

Using the Schwinger-Keldysh-formalism, reformulated in arXiv:2108.01695 as an effective field theory in Euclidean anti-de Sitter, we evaluate the one-loop cosmological four-point function of a conformally coupled interacting scalar field in de Sitter. Recasting the Witten cosmological correlator as flat space Feynman integrals, we evaluate the one-loop cosmological four-point functions in de Sitter space in terms of single-valued multiple polylogarithms. From it we derive anomalous dimensions and OPE coefficients of the dual conformal field theory at space-like, future infinity. In particular, we find an interesting degeneracy in the anomalous dimensions relating operators of neighboring spins.

arXiv comment47 pages. v2: minor corrections. Version published in JHEP

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• New recursions for tree-level correlators in (Anti) de Sitter space
• Continuous Spectrum on Cosmological Collider
• On Graviton non-Gaussianities in the Effective Field Theory of Inflation
• Effective Field Theories and Cosmological Scattering Equations
• The Geometry of Cosmological Correlators
• de Sitter at all loops: the story of the Schwinger model
• Analytic Formulae for Inflationary Correlators with Dynamical Mass
• All plus four point (A)dS graviton function using generalized on-shell recursion relation
• Cosmohedra
• On (spinor)-helicity and bosonization in $Ad{S}_4/CF{T}_3$
• Correlator Polytopes
• RG flows in de Sitter: c-functions and sum rules