Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation

Abstract

Using symmetry considerations, we derive Ward identities which relate the three point function of scalar perturbations produced during inflation to the scalar four point function, in a particular limit. The derivation assumes approximate conformal invariance, and the conditions for the slow roll approximation, but is otherwise model independent. The Ward identities allow us to deduce that the three point function must be suppressed in general, being of the same order of magnitude as in the slow roll model. They also fix the three point function in terms of the four point function, upto one constant which we argue is generically suppressed. Our approach is based on analyzing the wave function of the universe, and the Ward identities arise by imposing the requirements of spatial and time reparametrization invariance on it.

arXiv comment35 pages; Extra references and comments added, The version published in JHEP

References in corpus (36)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Single field consistency relation for the 3-point function
• Ghost Inflation
• On graviton non-Gaussianities during inflation
• On Soft Limits of Inflationary Correlation Functions
• Implications of conformal invariance in momentum space
• On the consistency relation of the 3-point function in single field inflation
• Conformal consistency relations for single-field inflation
• Conformal Symmetries of Adiabatic Modes in Cosmology
• An Infinite Set of Ward Identities for Adiabatic Modes in Cosmology
• CMB from CFT
• Operator Product Expansion of Inflationary Correlators and Conformal Symmetry of de Sitter
• Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evaluation of Feynman's Master Integrals
• Holography for inflation using conformal perturbation theory
• Conformal Invariance, Dark Energy, and CMB Non-Gaussianity
• Conformal Invariance and the Four Point Scalar Correlator in Slow-Roll Inflation
• Conformal Invariance and Cosmic Background Radiation
• A Note on the Consistency Condition of Primordial Fluctuations
• De Sitter Holography and the Cosmic Microwave Background
• Holographic predictions for cosmological 3-point functions
• Holographic Non-Gaussianity
• Slavnov-Taylor Identities for Primordial Perturbations
• Lifshitz holography: The whole shebang
• Inflation and de Sitter Holography
• The CMB bispectrum in the squeezed limit
• Consistency condition for inflation from (broken) conformal symmetry
• Cosmological 3-point correlators from holography
• Inflationary Consistency Conditions from a Wavefunctional Perspective
• Non-Gaussianity in the Cosmic Microwave Background Anisotropies at Recombination in the Squeezed limit
• The Four-point Correlator in Multifield Inflation, the Operator Product Expansion and the Symmetries of de Sitter
• The Physical Squeezed Limit: Consistency Relations at Order q^2
• On the scalar consistency relation away from slow roll
• Consistency Relations for the Conformal Mechanism
• Multiple Soft Limits of Cosmological Correlation Functions
• Double Soft Limits of Cosmological Correlations
• Examining the consistency relations describing the three-point functions involving tensors

Cited by in corpus (84)

• Non-Gaussianity as a Particle Detector
• Bootstrapping Inflationary Correlators in Mellin Space
• Cosmological Cutting Rules
• From AdS to dS Exchanges: Spectral Representation, Mellin Amplitudes and Crossing
• From dS to AdS and back
• Building a Boostless Bootstrap for the Bispectrum
• Cutting Cosmological Correlators
• From Locality and Unitarity to Cosmological Correlators
• Ward Identities for Scale and Special Conformal Transformations in Inflation
• Renormalised 3-point functions of stress tensors and conserved currents in CFT
• The Inflationary Wavefunction from Analyticity and Factorization
• From Planck data to Planck era: Observational tests of Holographic Cosmology
• Conformal $n$-point functions in momentum space
• The Boostless Bootstrap: Amplitudes without Lorentz boosts
• Renormalised CFT 3-point functions of scalars, currents and stress tensors
• Cosmological Bootstrap in Slow Motion
• On the time evolution of cosmological correlators
• Momentum space approach to crossing symmetric CFT correlators
• Shapes of gravity: Tensor non-Gaussianity and massive spin-2 fields
• CFT Unitarity and the AdS Cutkosky Rules
• A generalized non-Gaussian consistency relation for single field inflation
• Momentum-space conformal blocks on the light cone
• Conformal correlators as simplex integrals in momentum space
• Bootstrapping Large Graviton non-Gaussianities
• The Conformal Limit of Inflation in the Era of CMB Polarimetry
• High-Scale Inflation and the Tensor Tilt
• From Amplitudes to Contact Cosmological Correlators
• Momentum space conformal three-point functions of conserved currents and a general spinning operator
• Amplitudes meet Cosmology: A (Scalar) Primer
• Momentum space approach to crossing symmetric CFT correlators II: General spacetime dimension
• The graviton four-point function in de Sitter space
• Double copy structure of parity-violating CFT correlators
• Cancellation of quantum corrections on the soft curvature perturbations
• The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization
• Symmetry Constraints in Inflation, $\alpha$-vacua, and the Three Point Function
• The goldstone and goldstino of supersymmetric inflation
• Conformal 3-point functions and the Lorentzian OPE in momentum space
• A Differential Representation of Cosmological Wavefunctions
• Higher spin 3-point functions in 3d CFT using spinor-helicity variables
• Momentum space parity-odd CFT 3-point functions
• Momentum space spinning correlators and higher spin equations in three dimensions
• COSMOS-$e^{\prime }$- soft Higgsotic attractors
• Asymptotic Symmetries in de Sitter and Inflationary Spacetimes
• COSMOS-$e^{\prime }$-GTachyon from String Theory
• Systematics of Adiabatic Modes: Flat Universes
• Constraining momentum space correlators using slightly broken higher spin symmetry
• Renormalisation of IR divergences and holography in de Sitter
• Vanishing of local non-Gaussianity in canonical single field inflation
• Opacity from Loops in AdS
• The tensor bi-spectrum in a matter bounce
• On Graviton non-Gaussianities in the Effective Field Theory of Inflation
• On Holography in General Background and the Boundary Effective Action from AdS to dS
• Effective Field Theories and Cosmological Scattering Equations
• Constraining holographic cosmology using Planck data
• Constraining momentum space CFT correlators with consistent position space OPE limit and the collider bound
• Four-Point Functions in Momentum Space: Conformal Ward Identities in the Scalar/Tensor case
• Momentum space CFT correlators for Hamiltonian truncation
• Enhanced Soft Limits in de Sitter Space
• Large gauge transformation, Soft theorem, and Infrared divergence in inflationary spacetime
• Holography for the very early Universe and the classic puzzles of Hot Big Bang cosmology
• Rational Wavefunctions in de Sitter Spacetime
• Momentum space CFT correlators of non-conserved spinning operators
• Inflation and Conformal Invariance: The Perspective from Radial Quantization
• Wavefunctions in dS/CFT revisited: principal series and double-trace deformations
• Anyonic correlation functions in Chern-Simons matter theories
• Consistency relations in multi-field inflation
• The Boostless Bootstrap and BCFW Momentum Shifts
• Hysteresis in the Sky
• Unifying attractor and non-attractor models of inflation under a single soft theorem
• Spatial Curvature at the Sound Horizon
• Consistency relations and conservation of $\zeta$ in holographic inflation
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• A CFT interpretation of cosmological correlation functions in $\alpha -$vacua in de-Sitter space
• Holographic cosmology solutions of problems with pre-inflationary cosmology
• On the consistency of (partially-)massless matter couplings in de Sitter space
• Inflationary non-Gaussianities in alpha vacua and consistency with conformal symmetries
• Soft theorems in de Sitter spacetime
• Soft Limits of Gluon and Graviton Correlators in Anti-de Sitter Space
• A maximal-entropy initial state of the Universe as a microscopic description of inflation
• The primordial non-Gaussianities for non-singular Horndeski cosmologies
• Issues about Cosmological Ward Identities
• The double-soft limit in cosmological correlation functions and graviton exchange effects
• The scalar-scalar-tensor inflationary three-point function in the axion monodromy model
• Perturbative soft graviton theorems in de Sitter spacetime