On the Initial State and Consistency Relations

Abstract

We study the effect of the initial state on the consistency conditions for adiabatic perturbations. In order to be consistent with the constraints of General Relativity, the initial state must be diffeomorphism invariant. As a result, we show that initial wavefunctional/density matrix has to satisfy a Slavnov-Taylor identity similar to that of the action. We then investigate the precise ways in which modified initial states can lead to violations of the consistency relations. We find two independent sources of violations: i) the state can include initial non-Gaussianities; ii) even if the initial state is Gaussian, such as a Bogoliubov state, the modified 2-point function can modify the q->0 analyticity properties of the vertex functional and result in violations of the consistency relations.

25 pages; v2: refs added

References in corpus (77)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Generating the curvature perturbation without an inflaton
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• The Trans-Planckian Problem of Inflationary Cosmology
• Single field consistency relation for the 3-point function
• A new mechanism for generating density perturbations from inflation
• Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity
• A note on inflation and transplanckian physics
• The Robustness of Inflation to Changes in Super-Planck-Scale Physics
• Galilean Genesis: an alternative to inflation
• On Soft Limits of Inflationary Correlation Functions
• Enhanced Non-Gaussianity from Excited Initial States
• Signatures of Short Distance Physics in the Cosmic Microwave Background
• On the consistency relation of the 3-point function in single field inflation
• A generic estimate of trans-Planckian modifications to the primordial power spectrum in inflation
• Inflation with a Planck-scale frequency cutoff
• Perturbation spectrum in inflation with cutoff
• Conformal consistency relations for single-field inflation
• Mode Generating Mechanism in Inflation with Cutoff
• Signatures of Initial State Modifications on Bispectrum Statistics
• The Observed Squeezed Limit of Cosmological Three-Point Functions
• Trans-Planckian dispersion and scale-invariance of inflationary perturbations
• Single-Field Consistency Relations of Large Scale Structure
• Symmetries and Consistency Relations in the Large Scale Structure of the Universe
• Imprints of Short Distance Physics On Inflationary Cosmology
• Conformal Symmetries of Adiabatic Modes in Cosmology
• Probing String Theory with Modulated Cosmological Fluctuations
• 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
• Performance of jet substructure techniques for large-R jets in proton-proton collisions at sqrt(s) = 7 TeV using the ATLAS detector
• Are Inflationary Predictions Sensitive to Very High Energy Physics?
• Initial Conditions for Inflation
• The (not so) squeezed limit of the primordial 3-point function
• Rapidly-Varying Speed of Sound, Scale Invariance and Non-Gaussian Signatures
• Holography for inflation using conformal perturbation theory
• Inflation, holography, and the choice of vacuum in de Sitter space
• Calculating the local-type fNL for slow-roll inflation with a non-vacuum initial state
• Subluminal Galilean Genesis
• Effective field theory and non-Gaussianity from general inflationary states
• Harrison--Zeldovich spectrum from conformal invariance
• Reconciliation of High Energy Scale Models of Inflation with Planck
• Inflation with General Initial Conditions for Scalar Perturbations
• Is there an imprint of Planck scale physics on inflationary cosmology?
• Effective Field Theories and Inflation
• One-particle-irreducible consistency relations for cosmological perturbations
• On Squeezed Limits in Single-Field Inflation - Part I
• A Note on Calm Excited States of Inflation
• DBI Realizations of the Pseudo-Conformal Universe and Galilean Genesis Scenarios
• The Pseudo-Conformal Universe: Scale Invariance from Spontaneous Breaking of Conformal Symmetry
• Decoupling in an expanding universe: boundary RG-flow affects initial conditions for inflation
• Slavnov-Taylor Identities for Primordial Perturbations
• DBI Genesis: An Improved Violation of the Null Energy Condition
• Decoupling in an expanding universe: backreaction barely constrains short distance effects in the CMB
• The CMB bispectrum in the squeezed limit
• Consistency condition for inflation from (broken) conformal symmetry
• Bispectrum signatures of a modified vacuum in single field inflation with a small speed of sound
• Inflationary Consistency Conditions from a Wavefunctional Perspective
• Non-linear Realizations of Conformal Symmetry and Effective Field Theory for the Pseudo-Conformal Universe
• Defrosting in an Emergent Galileon Cosmology
• Non-Gaussianity in the Cosmic Microwave Background Anisotropies at Recombination in the Squeezed limit
• Soft-Pion Theorems for Large Scale Structure
• Non-Gaussianity from Excited Initial Inflationary States
• From Satisfying to Violating the Null Energy Condition
• Non-Gaussianity Consistency Relations, Initial States and Back-reaction
• Renormalization of initial conditions and the trans-Planckian problem of inflation
• Bounds on Generic High-Energy Physics Modifications to the Primordial Power Spectrum from Back-Reaction on the Metric
• 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
• Oscillations in the Primordial Bispectrum: Mode Expansion
• Non-Trivial Checks of Novel Consistency Relations
• Enhanced CMBR non-Gaussianities from Lorentz violation
• Searches for $B_{(s)}^0\to J/\psi p\overline{p}$ and $B^{+}\to J/\psi p\overline{p}{\pi }^{+}$ decays
• Effective Field Theory Approach to Cosmological Initial Conditions: Self-Consistency Bounds and Non-Gaussianities
• A Cosmological Slavnov-Taylor Identity
• Trans-Planckian enhancements of the primordial non-Gaussianities

Cited by in corpus (21)

• Consistently violating the non-Gaussian consistency relation
• Inflationary soft theorems revisited: A generalized consistency relation
• Multiple Soft Limits of Cosmological Correlation Functions
• Double Soft Limits of Cosmological Correlations
• The squeezed limit of the bispectrum in multi-field inflation
• Soft limits in holographic cosmology
• New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies
• CMB B-mode non-Gaussianity: optimal bispectrum estimator and Fisher forecasts
• Cosmological Perturbations and the Weinberg Theorem
• Revisiting non-Gaussianity in non-attractor inflation models in the light of the cosmological soft theorem
• The Separate Universe Approach to Soft Limits
• Large gauge transformation, Soft theorem, and Infrared divergence in inflationary spacetime
• A Cosmological Slavnov-Taylor Identity
• Robustness of inflation to kinetic inhomogeneities
• Conservation of $\zeta$ with radiative corrections from heavy field
• The galaxy bias at second order in general relativity with Non-Gaussian initial conditions
• First test of the consistency relation for the large-scale structure using the anisotropic three-point correlation function of BOSS DR12 galaxies (An explanatory video is available at https://youtu.be/Zi36ooLPhss.)
• General Covariance Constraints on Cosmological Correlators
• Inflation in Flatland
• CMB statistical anisotropies of classical and quantum origins
• Issues about Cosmological Ward Identities