Multiple Soft Limits of Cosmological Correlation Functions

Abstract

We derive novel identities satisfied by inflationary correlation functions in the limit where two external momenta are taken to be small. We derive these statements in two ways: using background-wave arguments and as Ward identities following from the fixed-time path integral. Interestingly, these identities allow us to constrain some of the O(q^2) components of the soft limit, in contrast to their single-soft analogues. We provide several nontrivial checks of our identities both in the context of resonant non-Gaussianities and in small sound speed models. Additionally, we extend the relation at lowest order in external momenta to arbitrarily many soft legs, and comment on the many-soft extension at higher orders in the soft momentum. Finally, we consider how higher soft limits lead to identities satisfied by correlation functions in large-scale structure.

39 pages, 2 figures. v2: minor corrections, added references. Version to appear in JCAP

References in corpus (83)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• The Effective Field Theory of Inflation
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Ghost Condensation and a Consistent Infrared Modification of Gravity
• Gravity Waves and Linear Inflation from Axion Monodromy
• Single field consistency relation for the 3-point function
• Starting the Universe: Stable Violation of the Null Energy Condition and Non-standard Cosmologies
• What is the Simplest Quantum Field Theory?
• The Effective Field Theory of Dark Energy
• On graviton non-Gaussianities during inflation
• Oscillations in the CMB from Axion Monodromy Inflation
• A Natural Framework for Chaotic Inflation
• Galilean Genesis: an alternative to inflation
• Adiabatic Modes in Cosmology
• On Soft Limits of Inflationary Correlation Functions
• Generation and Characterization of Large Non-Gaussianities in Single Field Inflation
• Enhanced Non-Gaussianity from Excited Initial States
• The Effective Theory of Quintessence: the w<-1 Side Unveiled
• On the consistency relation of the 3-point function in single field inflation
• Conformal consistency relations for single-field inflation
• Resonant Non-Gaussianity
• Signatures of Initial State Modifications on Bispectrum Statistics
• Single-Field Consistency Relations of Large Scale Structure
• Symmetries and Consistency Relations in the Large Scale Structure of the Universe
• Conformal Symmetries of Adiabatic Modes in Cosmology
• The Inflationary Trispectrum for Models with Large Non-Gaussianities
• Non-gaussianities and the Stimulated creation of quanta in the inflationary universe
• An Infinite Set of Ward Identities for Adiabatic Modes in Cosmology
• Galilean invariance and the consistency relation for the nonlinear squeezed bispectrum of large scale structure
• A Single Field Inflation Model with Large Local Non-Gaussianity
• CMB from CFT
• Performance of jet substructure techniques for large-R jets in proton-proton collisions at sqrt(s) = 7 TeV using the ATLAS detector
• Operator Product Expansion of Inflationary Correlators and Conformal Symmetry of de Sitter
• Rapidly-Varying Speed of Sound, Scale Invariance and Non-Gaussian Signatures
• Holography for inflation using conformal perturbation theory
• Conformal Invariance and the Four Point Scalar Correlator in Slow-Roll Inflation
• Non-Gaussianity in a Matter Bounce
• Calculating the local-type fNL for slow-roll inflation with a non-vacuum initial state
• Conformal invariance of scalar perturbations in inflation
• Subluminal Galilean Genesis
• Effective field theory and non-Gaussianity from general inflationary states
• Harrison--Zeldovich spectrum from conformal invariance
• Inflation with General Initial Conditions for Scalar Perturbations
• On the full trispectrum in single field DBI-inflation
• Reconciliation of High Energy Scale Models of Inflation with Planck
• Conformal Invariance and Cosmic Background Radiation
• A Note on the Consistency Condition of Primordial Fluctuations
• One-particle-irreducible consistency relations for cosmological perturbations
• On Squeezed Limits in Single-Field Inflation - Part I
• (Small) Resonant non-Gaussianities: Signatures of a Discrete Shift Symmetry in the Effective Field Theory of Inflation
• A Note on Calm Excited States of Inflation
• Holographic predictions for cosmological 3-point functions
• DBI Realizations of the Pseudo-Conformal Universe and Galilean Genesis Scenarios
• The Pseudo-Conformal Universe: Scale Invariance from Spontaneous Breaking of Conformal Symmetry
• Inflationary tensor fossils in large-scale structure
• DBI Genesis: An Improved Violation of the Null Energy Condition
• Slavnov-Taylor Identities for Primordial Perturbations
• Single-Field Consistency Relations of Large Scale Structure. Part II: Resummation and Redshift Space
• Single-Field Consistency Relations of Large Scale Structure. Part III: Test of the Equivalence Principle
• Cosmological 3-point correlators from holography
• Consistency condition for inflation from (broken) conformal symmetry
• Consequences of Symmetries and Consistency Relations in the Large-Scale Structure of the Universe for Non-local bias and Modified Gravity
• Inflationary Consistency Conditions from a Wavefunctional Perspective
• Non-linear Realizations of Conformal Symmetry and Effective Field Theory for the Pseudo-Conformal Universe
• Action approach to cosmological perturbations: the 2nd order metric in matter dominance
• Ward identities and consistency relations for the large scale structure with multiple species
• Resonant Trispectrum and a Dozen More Primordial N-point functions
• Soft-Pion Theorems for Large Scale Structure
• Non-Gaussianity from Excited Initial Inflationary States
• The Physical Squeezed Limit: Consistency Relations at Order q^2
• Consistency Relations for the Conformal Mechanism
• Non-Gaussianities in the Cosmological Perturbation Spectrum due to Primordial Anisotropy
• Non-Gaussianities in the Cosmological Perturbation Spectrum due to Primordial Anisotropy II
• Kinematic consistency relations of large-scale structures
• Cosmological density perturbations from conformal scalar field: infrared properties and statistical anisotropy
• Non-Trivial Checks of Novel Consistency Relations
• On the Initial State and Consistency Relations
• Enhanced CMBR non-Gaussianities from Lorentz violation
• Non-supersymmetric Microstates of the MSW System
• The consistency condition for the three-point function in dissipative single-clock inflation
• Searches for $B_{(s)}^0\to J/\psi p\overline{p}$ and $B^{+}\to J/\psi p\overline{p}{\pi }^{+}$ decays
• Squeezed primordial bispectrum from general vacuum state
• Trans-Planckian enhancements of the primordial non-Gaussianities

Cited by in corpus (25)

• Spacetime structure near generic horizons and soft hair
• Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation
• Ward Identities for Scale and Special Conformal Transformations in Inflation
• Inflationary soft theorems revisited: A generalized consistency relation
• Landscape tomography through primordial non-Gaussianity
• Symmetry Constraints in Inflation, $\alpha$-vacua, and the Three Point Function
• Is There Scale-Dependent Bias in Single-Field Inflation?
• Double-soft graviton amplitudes and the extended BMS charge algebra
• Double Soft Limits of Cosmological Correlations
• The squeezed limit of the bispectrum in multi-field inflation
• Non-Trivial Checks of Novel Consistency Relations
• Soft limits in holographic cosmology
• Cosmic variance in inflation with two light scalars
• CMB Anisotropies from a Gradient Mode
• Violation of the consistency relations for large-scale structure with dark energy
• The Separate Universe Approach to Soft Limits
• Weinberg Soft Theorems from Weinberg Adiabatic Modes
• Inflation and Conformal Invariance: The Perspective from Radial Quantization
• Non-Gaussian CMB and LSS statistics beyond polyspectra
• Soft theorems for boosts and other time symmetries
• Conservation of $\zeta$ with radiative corrections from heavy field
• Non-local bispectra from super cosmic variance
• Inflation in Flatland
• The double-soft limit in cosmological correlation functions and graviton exchange effects
• On the space of non-Gaussian fields with single-clock bispectra