A new method for calculating the primordial bispectrum in the squeezed limit

Abstract

In 2004, Creminelli and Zaldarriaga proposed a consistency relation for the primordial curvature perturbation of all single-field inflation models; it related the bispectrum in the squeezed limit to the spectral tilt. We have developed a technique, based in part on the Creminelli and Zaldarriaga argument, that can greatly simplify the calculation of the squeezed-limit bispectrum using the in-in formalism; we were able to arrive at a generic formula that does not rely on a slow-roll approximation. Using our formula, we explicitly tested the consistency relation for power-law inflation and for an exactly scale-invariant model by Starobinsky; for the latter model, Creminelli and Zaldarriaga's argument predicts a vanishing bispectrum whereas our quantum calculation shows a non-zero bispectrum that approaches zero in the long-wavelength limit and for inflation with a large number of e-folds.

24 pages, 0 figures; v3: added a section calculating the squeezed limit bispectrum of a model by Starobinsky, accepted by JCAP; v2: refocused paper on main result, improved proof of consistency relation, added some references

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• Calculating the local-type fNL for slow-roll inflation with a non-vacuum initial state
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• Inflation with General Initial Conditions for Scalar Perturbations
• In-in and $\delta N$ calculations of the bispectrum from non-attractor single-field inflation
• A Note on the Consistency Condition of Primordial Fluctuations
• Shapes of primordial non-Gaussianities in the Horndeski's most general scalar-tensor theories
• Consistently violating the non-Gaussian consistency relation
• A generalized non-Gaussian consistency relation for single field inflation
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• Hemispherical Asymmetry and Local non-Gaussianity: a Consistency Condition
• Inflationary soft theorems revisited: A generalized consistency relation
• Non-Gaussianity Consistency Relation for Multi-field Inflation
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• On the squeezed limit of the bispectrum in general single field inflation
• Non-Gaussianities in Multifield Inflation: Superhorizon Evolution, Adiabaticity, and the Fate of fnl
• Non-Gaussianities and tensor-to-scalar ratio in non-local $R^2$-like inflation
• Non-Gaussianity in single field models without slow-roll
• Perturbative Reheating After Multiple-Field Inflation: The Impact on Primordial Observables
• Examining the consistency relations describing the three-point functions involving tensors
• Vanishing of local non-Gaussianity in canonical single field inflation
• The tensor bi-spectrum in a matter bounce
• A Consistency Relation for Single-Field Inflation with Power Spectrum Oscillations
• Probing correlations of early magnetic fields using mu-distortion
• Tensor to scalar ratio and large scale power suppression from pre-slow roll initial conditions
• Consistency Relation for multifield inflation scenario with all loop contributions
• Correlating CMB Spectral Distortions with Temperature: what do we learn on Inflation?
• Primordial Stochastic Gravitational Wave Background Anisotropies: in-in Formalization and Applications
• Scale-dependent hemispherical asymmetry from general initial state during inflation
• Conservation of $\zeta$ with radiative corrections from heavy field
• Consistency relation and inflaton field redefinition in the delta N formalism
• Extracting the size of the cosmic electron-positron anomaly
• Non-Gaussianity from Compositeness
• The spatial gauge-dependence of single-field inflationary bispectra
• Quantitative classicality in cosmological interactions during inflation
• The primordial non-Gaussianities for non-singular Horndeski cosmologies
• The scalar-scalar-tensor inflationary three-point function in the axion monodromy model
• Inflationary cross-correlations of a non-minimal spectator and their soft limits
• Aspects of inflation and the very early universe