An Infinite Set of Ward Identities for Adiabatic Modes in Cosmology

Abstract

We show that the correlation functions of any single-field cosmological model with constant growing-modes are constrained by an infinite number of novel consistency relations, which relate (N+1)-point correlation functions with a soft-momentum scalar or tensor mode to a symmetry transformation on N-point correlation functions of hard-momentum modes. We derive these consistency relations from Ward identities for an infinite tower of non-linearly realized global symmetries governing scalar and tensor perturbations. These symmetries can be labeled by an integer n. At each order n, the consistency relations constrain - completely for n=0,1, and partially for n>= 2 - the q^n behavior of the soft limits. The identities at n=0 recover Maldacena's original consistency relations for a soft scalar and tensor mode, n=1 gives the recently-discovered conformal consistency relations, and the identities for n>= 2 are new. As a check, we verify directly that the n=2 identity is satisfied by known correlation functions in slow-roll inflation.

47 pages. v3 typos corrected, matches published version

References in corpus (33)

• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• New Ekpyrotic Cosmology
• Galilean Genesis: an alternative to inflation
• Quantum Contributions to Cosmological Correlations II: Can These Corrections Become Large?
• Enhanced Non-Gaussianity from Excited Initial States
• Solid Inflation
• On the consistency relation of the 3-point function in single field inflation
• Generating Ekpyrotic Curvature Perturbations Before the Big Bang
• Conformal Symmetries of Adiabatic Modes in Cosmology
• CMB from CFT
• Symmetries and Loops in Inflation
• Holography for inflation using conformal perturbation theory
• Non-Gaussianity in a Matter Bounce
• Subluminal Galilean Genesis
• Effective field theory and non-Gaussianity from general inflationary states
• Harrison--Zeldovich spectrum from conformal invariance
• The constancy of ζin single-clock Inflation at all loops
• One-particle-irreducible consistency relations for cosmological perturbations
• On Squeezed Limits in Single-Field Inflation - Part I
• DBI Realizations of the Pseudo-Conformal Universe and Galilean Genesis Scenarios
• DBI Genesis: An Improved Violation of the Null Energy Condition
• Speedy sound and cosmic structure
• Consistency condition for inflation from (broken) conformal symmetry
• Resonant Trispectrum and a Dozen More Primordial N-point functions
• The Four-point Correlator in Multifield Inflation, the Operator Product Expansion and the Symmetries of de Sitter
• Non-Gaussianity from Excited Initial Inflationary States
• Generating Scale-Invariant Perturbations from Rapidly-Evolving Equation of State
• Consistency Relations for the Conformal Mechanism
• Near Scale Invariance with Modified Dispersion Relations
• Towards a Cosmological Dual to Inflation
• Seeding of Primordial Perturbations During a Decelerated Expansion
• Scale Invariance via a Phase of Slow Expansion
• On Primordial Density Perturbation and Decaying Speed of Sound

Cited by in corpus (127)

• Non-Gaussianity as a Particle Detector
• Spacetime structure near generic horizons and soft hair
• The $\Lambda$-BMS${}_4$ Charge Algebra
• Conformal Invariance and the Four Point Scalar Correlator in Slow-Roll Inflation
• Building a Boostless Bootstrap for the Bispectrum
• Linking the Singularities of Cosmological Correlators
• Parity breaking signatures from a Chern-Simons coupling during inflation: the case of non-Gaussian gravitational waves
• Partially Massless Fields During Inflation
• A Hidden Symmetry of the Galileon
• Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation
• Imprints of Massive Primordial Fields on Large-Scale Structure
• Ward Identities for Scale and Special Conformal Transformations in Inflation
• Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities
• On Separate Universes
• Galaxy Bispectrum from Massive Spinning Particles
• Inflationary tensor fossils in large-scale structure
• Slavnov-Taylor Identities for Primordial Perturbations
• Soft de Sitter Effective Theory
• Soft Theorems For Shift-Symmetric Cosmologies
• A generalized non-Gaussian consistency relation for single field inflation
• Inflationary Consistency Conditions from a Wavefunctional Perspective
• Tensor Squeezed Limits and the Higuchi Bound
• The squeezed limit of the solid inflation three-point function
• Ward identities and consistency relations for the large scale structure with multiple species
• Charge Algebra in Al(A)dS${}_n$ Spacetimes
• Shift Symmetries in (Anti) de Sitter Space
• On the Symmetries of Cosmological Perturbations
• The Conformal Limit of Inflation in the Era of CMB Polarimetry
• How Gaussian can our Universe be?
• From Amplitudes to Contact Cosmological Correlators
• Soft-Pion Theorems for Large Scale Structure
• Primordial Gravitational Waves from Galaxy Intrinsic Alignments
• Conformal Fermi Coordinates
• Amplitudes meet Cosmology: A (Scalar) Primer
• Inflationary soft theorems revisited: A generalized consistency relation
• The graviton four-point function in de Sitter space
• The Effective Theory of Shift-Symmetric Cosmologies
• The Hunt for Primordial Interactions in the Large Scale Structures of the Universe
• Cancellation of quantum corrections on the soft curvature perturbations
• Searching for Fossil Fields in the Gravity Sector
• Tensor non-Gaussianity in chiral scalar-tensor theories of gravity
• Symmetry Constraints in Inflation, $\alpha$-vacua, and the Three Point Function
• A Consistency Relation for the Observed Galaxy Bispectrum and the Local non-Gaussianity from Relativistic Corrections
• Testing the Early Universe with Anisotropies of the Gravitational Wave Background
• Probing the inflationary particle content: extra spin-2 field
• Double-soft graviton amplitudes and the extended BMS charge algebra
• The Cosmological Phonon: Symmetries and Amplitudes on Sub-Horizon Scales
• Asymptotic Symmetries in de Sitter and Inflationary Spacetimes
• Multiple Soft Limits of Cosmological Correlation Functions
• COSMOS-$e^{\prime }$-GTachyon from String Theory
• Systematics of Adiabatic Modes: Flat Universes
• Double Soft Limits of Cosmological Correlations
• The squeezed limit of the bispectrum in multi-field inflation
• Vanishing of local non-Gaussianity in canonical single field inflation
• Soft limits in holographic cosmology
• Cosmic variance in inflation with two light scalars
• Non-Trivial Checks of Novel Consistency Relations
• On Graviton non-Gaussianities in the Effective Field Theory of Inflation
• On the Initial State and Consistency Relations
• CMB Anisotropies from a Gradient Mode
• Non-trivial gravitational waves and structure formation phenomenology from dark energy
• Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach
• CMB B-mode non-Gaussianity: optimal bispectrum estimator and Fisher forecasts
• Solid Soft Theorems
• Violation of the consistency relations for large-scale structure with dark energy
• Solid Consistency
• Effective Field Theories and Cosmological Scattering Equations
• Quadrupolar radiation in de Sitter: Displacement memory and Bondi metric
• Small-scale Tests of Inflation
• Possible Signatures of Inflationary Particle Content: Spin-2 Fields
• A non-perturbative test of consistency relations and their violation
• Improvement of energy-momentum tensor and non-Gaussianities in holographic cosmology
• The Separate Universe Approach to Soft Limits
• Enhanced Soft Limits in de Sitter Space
• Squeezing $f_{\mathrm{NL}}$ out of the matter bispectrum with consistency relations
• Large gauge transformation, Soft theorem, and Infrared divergence in inflationary spacetime
• Patient Observers and Non-perturbative Infrared Dynamics in Inflation
• Effective Theory of Squeezed Correlation Functions
• Lagrangian space consistency relation for large scale structure
• Holographic non-Gaussianities in general single-field inflation
• On Soft Limits of Large-Scale Structure Correlation Functions
• A Cosmological Slavnov-Taylor Identity
• KLT-Like Behaviour of Inflationary Graviton Correlators
• Anisotropic separate universe and Weinberg's adiabatic mode
• Primordial Stochastic Gravitational Wave Background Anisotropies: in-in Formalization and Applications
• Asymptotic symmetries in spatially flat FRW
• Consistency relations in multi-field inflation
• Primordial Non-Gaussianity in Supersolid Inflation
• An Effective Theory for Holographic RG Flows
• Strolling along gauge theory vacua
• Soft theorems for boosts and other time symmetries
• Consistency relations and conservation of $\zeta$ in holographic inflation
• Conservation of $\zeta$ with radiative corrections from heavy field
• Unifying attractor and non-attractor models of inflation under a single soft theorem
• Spatial Curvature at the Sound Horizon
• Non-local bispectra from super cosmic variance
• General Covariance Constraints on Cosmological Correlators
• Holography for a Non-Inflationary Early Universe
• Inflation in Flatland
• The Physical Content of Long Tensor Modes in Cosmology
• Gravitational multipole moments for asymptotically de Sitter spacetimes
• On the primordial correlation of gravitons with gauge fields
• Shift Symmetries and AdS/CFT
• Inflationary non-Gaussianities in alpha vacua and consistency with conformal symmetries
• Super-Hawking Radiation
• Soft theorems in de Sitter spacetime
• Soft Limits of Gluon and Graviton Correlators in Anti-de Sitter Space
• Large gauge transformations, local coordinates and cosmological observables
• Asymptotic symmetries and memories of gauge theories in FLRW spacetimes
• Asymptotic symmetries of three dimensional gravity and the membrane paradigm
• Causality Implies Inflationary Back-Reaction
• Asymptotic dynamics and charges for FLRW spacetimes
• Issues about Cosmological Ward Identities
• A Consistency Relation for the CMB B-mode Polarization in the Squeezed Limit
• Is Patience a Virtue? Cosmic Censorship of Infrared Effects in de Sitter
• A Match Made in Heaven: Linking Observables in Inflationary Cosmology
• Baryonic effects in the Effective Field Theory of Large-Scale Structure and an analytic recipe for lensing in CMB-S4
• The double-soft limit in cosmological correlation functions and graviton exchange effects
• Inflationary cross-correlations of a non-minimal spectator and their soft limits
• A (semi)-exact Hamiltonian for the curvature perturbation $\zeta$
• Primordial fluctuations in extended Liouville theory
• Perturbative soft graviton theorems in de Sitter spacetime
• Spatial anisotropies from long wavelength scalar and tensor modes
• A Tail of Eternal Inflation
• Non-Gaussianity in the Squeezed Three-Point Correlation from the Relativistic Effects
• Inflationary spectral tilts as a result of the dilatation symmetry breaking
• On the space of non-Gaussian fields with single-clock bispectra