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.

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

References in corpus (16)

• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Enhanced Non-Gaussianity from Excited Initial States
• On the consistency relation of the 3-point function in single field inflation
• Conformal Symmetries of Adiabatic Modes in Cosmology
• Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation
• A Note on Calm Excited States of Inflation
• BCFW for Witten Diagrams
• Holographic Non-Gaussianity
• Consistency condition for inflation from (broken) conformal symmetry
• Cosmological 3-point correlators from holography
• On the scalar consistency relation away from slow roll
• 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

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