Closed-Form Formulae for Inflation Correlators

Abstract

We derive exact and closed-form expressions for a large class of two-point and three-point inflation correlators with the tree-level exchange of a single massive particle. The intermediate massive particle is allowed to have arbitrary mass, spin, chemical potential, and arbitrary nonderivative or derivative couplings to external inflaton modes. We also allow the coupling coefficients to have arbitrary complex power dependences on the conformal time. Our results feature closed-form expressions involving only familiar special functions and without any infinite sums. This is achieved by an improved bootstrap method with a suitable change of variables. Our results cover a wide range of cosmological collider models and can be directly used for future phenomenological studies. Our results can also be used as basic building blocks for constructing more complicated inflation correlators.

arXiv comment41 pages

References in corpus (78)

• Quantum Contributions to Cosmological Correlations
• Quasi-Single Field Inflation and Non-Gaussianities
• Signatures of Supersymmetry from the Early Universe
• Large non-Gaussianities with Intermediate Shapes from Quasi-Single Field Inflation
• Effective field theory approach to quasi-single field inflation and effects of heavy fields
• Non-Gaussianity as a Particle Detector
• Bootstrapping Inflationary Correlators in Mellin Space
• Quasi-Single Field Inflation with Large Mass
• The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds
• A Mellin Space Approach to Cosmological Correlators
• The Cosmological Optical Theorem
• Analyticity and Unitarity for Cosmological Correlators
• Schwinger-Keldysh Diagrammatics for Primordial Perturbations
• Cosmological Cutting Rules
• From AdS to dS Exchanges: Spectral Representation, Mellin Amplitudes and Crossing
• From dS to AdS and back
• Standard Model Background of the Cosmological Collider
• Curvature Perturbation Spectrum in Two-field Inflation with a Turning Trajectory
• Building a Boostless Bootstrap for the Bispectrum
• Linking the Singularities of Cosmological Correlators
• Cutting Cosmological Correlators
• Loop Corrections to Standard Model Fields in Inflation
• From Locality and Unitarity to Cosmological Correlators
• Heavy-Lifting of Gauge Theories By Cosmic Inflation
• Standard Model Mass Spectrum in Inflationary Universe
• Equilateral non-Gaussianity from heavy fields
• In Search of Large Signals at the Cosmological Collider
• Probing P and CP Violations on the Cosmological Collider
• Quasi Single Field Inflation in the non-perturbative regime
• The Inflationary Wavefunction from Analyticity and Factorization
• Boostless Cosmological Collider Bootstrap
• The Boostless Bootstrap: Amplitudes without Lorentz boosts
• Cosmological Collider Physics and the Curvaton
• Neutrino Signatures in Primordial Non-Gaussianities
• Searches for other vacua II: A new Higgstory at the cosmological collider
• Cosmological Bootstrap in Slow Motion
• A Cosmological Higgs Collider
• The Scalar Chemical Potential in Cosmological Collider Physics
• Seeing Higher-Dimensional Grand Unification In Primordial Non-Gaussianities
• Bootstrapping Multi-Field Inflation: non-Gaussianities from light scalars revisited
• Higher Spin Supersymmetry at the Cosmological Collider: Sculpting SUSY Rilles in the CMB
• Gauge Boson Signals at the Cosmological Collider
• Parity violation in the scalar trispectrum: no-go theorems and yes-go examples
• Minimal signatures of the Standard Model in non-Gaussianities
• Large Spin-2 Signals at the Cosmological Collider
• Phase Information in Cosmological Collider Signals
• Cutting Rule for Cosmological Collider Signals: A Bulk Evolution Perspective
• Non-Gaussian Enhancements of Galactic Halo Correlations in Quasi-Single Field Inflation
• Probing Leptogenesis with the Cosmological Collider
• Colliding Ghosts: Constraining Inflation with the Parity-Odd Galaxy Four-Point Function
• Helical Inflation Correlators: Partial Mellin-Barnes and Bootstrap Equations
• Cosmological Scattering Equations
• Bootstrapping Large Graviton non-Gaussianities
• Bootstrapping One-Loop Inflation Correlators with the Spectral Decomposition
• Strongly Coupled Quasi-Single Field Inflation
• From Amplitudes to Contact Cosmological Correlators
• Large-Field Inflation and the Cosmological Collider
• Precision Calculation of Inflation Correlators at One Loop
• Missing Scalars at the Cosmological Collider
• Cosmological Signatures of Superheavy Dark Matter
• Cosmological Collider Signatures of Massive Vectors from Non-Gaussian Gravitational Waves
• Inflationary flavor oscillations and the cosmic spectroscopy
• Classical Cosmological Collider Physics and Primordial Features
• Parity-Odd and Even Trispectrum from Axion Inflation
• Unique Fingerprints of Alternatives to Inflation in the Primordial Power Spectrum
• Towards the higher point holographic momentum space amplitudes II: Gravitons
• Disentangling mass spectra of multiple fields in cosmological collider
• On the inflationary massive field with a curved field manifold
• Quantum Standard Clocks in the Primordial Trispectrum
• Warm Quasi-Single Field Inflation
• Cosmological Scattering Equations at Tree-level and One-loop
• Axion Isocurvature Collider
• On spinning loop amplitudes in Anti-de Sitter space
• Analytical evaluation of cosmological correlation functions
• Heavy Particle Signatures in Cosmological Correlation Functions with Tensor Modes
• Gravitational Wave Probes of Massive Gauge Bosons at the Cosmological Collider
• A Cosmic Microscope for the Preheating Era
• On the consistency of (partially-)massless matter couplings in de Sitter space

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• Perturbative unitarity bounds on field-space curvature in de Sitter spacetime: purity vs scattering amplitude
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