A Mellin Space Approach to Cosmological Correlators

Abstract

We propose a Mellin space approach to the evaluation of late-time momentum-space correlation functions of quantum fields in $\left(d+1\right)$-dimensional de Sitter space. The Mellin-Barnes representation makes manifest the analytic structure of late-time correlators and, more generally, provides a convenient general $d$ framework for the study of conformal correlators in momentum space. In this work we focus on tree-level correlation functions of general scalars as a prototype, including $n$-point contact diagrams and $4$-point exchanges. For generic scalars, both the contact and exchange diagrams are given by (generalised) Hypergeometric functions, which reduce to existing expressions available in the literature for $d=3$ and external scalars which are either simultaneously conformally coupled or massless. This approach can also be used for the perturbative bulk evaluation of momentum-space boundary correlators in $\left(d+1\right)$-dimensional anti-de Sitter space (Witten diagrams).

arXiv comment44+14 pages, 9 figures

References in corpus (69)

• Gauge Theory Correlators from Non-Critical String Theory
• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Quantum Contributions to Cosmological Correlations
• Primordial Non-Gaussianities from Inflation Models
• Writing CFT correlation functions as AdS scattering amplitudes
• On graviton non-Gaussianities during inflation
• Implications of conformal invariance in momentum space
• De Sitter Space and Eternity
• A Natural Language for AdS/CFT Correlators
• Non-Gaussianities in models with a varying inflaton decay rate
• Spinning AdS Propagators
• Effective field theory approach to quasi-single field inflation and effects of heavy fields
• Non-Gaussianity as a Particle Detector
• Two-point Functions and Quantum Fields in de Sitter Universe
• The Angular Dependence of the Three-Point Correlation Function of the Cosmic Microwave Background Radiation as Predicted by Inflationary Cosmologies
• Towards Feynman rules for Mellin amplitudes in AdS/CFT
• Analyticity and the Holographic S-Matrix
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory
• De Sitter Musings
• CMB from CFT
• Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies
• Schwinger-Keldysh Diagrammatics for Primordial Perturbations
• Lecture notes on interacting quantum fields in de Sitter space
• Late-time Structure of the Bunch-Davies De Sitter Wavefunction
• Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evaluation of Feynman's Master Integrals
• Conformal Invariance, Dark Energy, and CMB Non-Gaussianity
• Higher-spin Interactions from CFT: The Complete Cubic Couplings
• Conformal Invariance and the Four Point Scalar Correlator in Slow-Roll Inflation
• Dissipative effects in the Effective Field Theory of Inflation
• Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
• A Study of Quantum Field Theories in AdS at Finite Coupling
• Double copy structure of CFT correlators
• Conformal invariance of scalar perturbations in inflation
• On Higher Spin Gauge Theory and the Critical O(N) Model
• Renormalised 3-point functions of stress tensors and conserved currents in CFT
• Spinning Witten Diagrams
• Renormalised CFT 3-point functions of scalars, currents and stress tensors
• Mixed-symmetry fields in de Sitter space: a group theoretical glance
• On Squeezed Limits in Single-Field Inflation - Part I
• BCFW for Witten Diagrams
• Spinning AdS Loop Diagrams: Two Point Functions
• Momentum space approach to crossing symmetric CFT correlators
• Non-gaussianity of inflationary field perturbations from the field equation
• Shapes of gravity: Tensor non-Gaussianity and massive spin-2 fields
• Evaluation of conformal integrals
• The group approach to AdS space propagators
• Non-Gaussianity from Excited Initial Inflationary States
• Momentum space conformal three-point functions of conserved currents and a general spinning operator
• New relation for AdS amplitudes
• Exact Correlators from Conformal Ward Identities in Momentum Space and the Perturbative $TJJ$ Vertex
• Anatomy of Geodesic Witten Diagrams
• Group theoretical approach to quantum fields in de Sitter space I. The principal series
• On the Perturbative Stability of Quantum Field Theories in de Sitter Space
• The large $N_c$ limit of four-point functions in N=4 super-Yang-Mills theory from anti-de Sitter Supergravity
• Geodesic Diagrams, Gravitational Interactions & OPE Structures
• High Energy Physics Signatures from Inflation and Conformal Symmetry of de Sitter
• AdS Weight Shifting Operators
• Group theoretical approach to quantum fields in de Sitter space II. The complementary and discrete series
• On Some Hypergeometric Solutions of the Conformal Ward Identities of Scalar 4-point Functions in Momentum Space
• The General 3-Graviton Vertex ($TTT$) of Conformal Field Theories in Momentum Space in $d=4$
• High order correlation functions for self interacting scalar field in de Sitter space
• Double-Trace Deformations of Conformal Correlations
• Renormalization, Conformal Ward Identities and the Origin of a Conformal Anomaly Pole
• Fermions in Geodesic Witten Diagrams
• Quantum Theory on Lobatchevski Spaces
• Geodesic Witten diagrams with anti-symmetric exchange
• KLT-Like Behaviour of Inflationary Graviton Correlators
• Operator Method and Recursion Relations for Inflationary Correlator

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