Symmetry Constraints in Inflation, $\alpha$-vacua, and the Three Point Function

Abstract

The Ward identities for conformal symmetries in single field models of inflation are studied in more detail in momentum space. For a class of generalized single field models, where the inflaton action contains arbitrary powers of the scalar and its first derivative, we find that the Ward identities are valid. We also study a one-parameter family of vacua, called $\alpha$-vacua, which preserve conformal invariance in de Sitter space. We find that the Ward identities, upto contact terms, are met for the three point function of a scalar field in the probe approximation in these vacua. Interestingly, the corresponding non-Gaussian term in the wave function does not satisfy the operator product expansion. For scalar perturbations in inflation, in the $\alpha$-vacua, we find that the Ward identities are not satisfied. We argue that this is because the back-reaction on the metric of the full quantum stress tensor has not been self-consistently incorporated. We also present a calculation, drawing on techniques from the AdS/CFT correspondence, for the three point function of scalar perturbations in inflation in the Bunch-Davies vacuum.

arXiv comment51 pages, 3 figures, 6 appendices. v3: JHEP version. Minor typos corrected

References in corpus (53)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• k-Inflation
• Perturbations in k-inflation
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Single field consistency relation for the 3-point function
• On graviton non-Gaussianities during inflation
• Adiabatic Modes in Cosmology
• On Soft Limits of Inflationary Correlation Functions
• Implications of conformal invariance in momentum space
• Enhanced Non-Gaussianity from Excited Initial States
• 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
• Initial Conditions for Inflation
• 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
• Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation
• Ward Identities for Scale and Special Conformal Transformations in Inflation
• Inflation with General Initial Conditions for Scalar Perturbations
• 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
• De Sitter Holography and the Cosmic Microwave Background
• A note on alpha-vacua and interacting field theory in de Sitter space
• A Note on Calm Excited States of Inflation
• BCFW for Witten Diagrams
• Holographic predictions for cosmological 3-point functions
• Holographic Non-Gaussianity
• Slavnov-Taylor Identities for Primordial Perturbations
• The CMB bispectrum in the squeezed limit
• Inflation and de Sitter Holography
• Cosmological 3-point correlators from holography
• Consistency condition for inflation from (broken) conformal symmetry
• 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
• Non-Gaussianity from Excited Initial Inflationary States
• Non-Gaussianity Consistency Relations, Initial States and Back-reaction
• The Physical Squeezed Limit: Consistency Relations at Order q^2
• On the scalar consistency relation away from slow roll
• High Energy Physics Signatures from Inflation and Conformal Symmetry of de Sitter
• Consistency Relations for the Conformal Mechanism
• Multiple Soft Limits of Cosmological Correlation Functions
• Examining the consistency relations describing the three-point functions involving tensors
• Double Soft Limits of Cosmological Correlations
• Soft limits in holographic cosmology
• The Cosmological Slavnov-Taylor Identity from BRST Symmetry in Single-Field Inflation
• The scalar-scalar-tensor inflationary three-point function in the axion monodromy model

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• Holographic Entanglement Entropy in the FLRW Universe
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• Inflationary non-Gaussianities in alpha vacua and consistency with conformal symmetries
• Quantum Fisher information of a cosmic qubit undergoing non-Markovian de Sitter evolution
• Stochastic gravitational wave background anisotropies from inflation with non-Bunch-Davies states
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