The full squeezed CMB bispectrum from inflation

Abstract

The small-scale CMB temperature we observe on the sky is modulated by perturbations that were super-horizon at recombination, giving differential focussing and lensing that generate a non-zero bispectrum even for single-field inflation where local physics is identical. Understanding this signal is important for primordial non-Gaussianity studies and also parameter constraints from the CMB lensing bispectrum signal. Because of cancellations individual effects can appear larger or smaller than they are in total, so a full analysis may be required to avoid biases. I relate angular scales on the sky to physical scales at recombination using the optical equations, and give full-sky results for the large-scale adiabatic temperature bispectrum from Ricci focussing (expansion of the ray bundle), Weyl lensing (convergence and shear), and temperature redshift modulations of small-scale power. The delta N expansion of the beam is described by the constant temperature 3-curvature, and gives a nearly-observable version of the consistency relation prediction from single-field inflation. I give approximate arguments to quantify the likely importance of dynamical effects, and argue that they can be neglected for modulation scales l <~ 100, which is sufficient for lensing studies and also allows robust tests of local primordial non-Gaussianity using only the large-scale modulation modes. For accurate numerical results early and late-time ISW effects must be accounted for, though I confirm that the late-time non-linear Rees-Sciama contribution is negligible compared to other more important complications. The total corresponds to f_NL ~ 7 for Planck-like temperature constraints and f_NL ~ 11 for cosmic-variance limited data to lmax=2000. Temperature lensing bispectrum estimates are affected at the 0.2 sigma level by Ricci focussing, and up to 0.5 sigma with polarization.

12 pages, 5 figures; typos corrected, minor edits

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• Anisotropies and non-Gaussianity of the Cosmological Gravitational Wave Background
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• DEMNUni: ISW, Rees-Sciama, and weak-lensing in the presence of massive neutrinos
• Anisotropic imprint of long-wavelength tensor perturbations on cosmic structure
• The intrinsic bispectrum of the Cosmic Microwave Background [PhD thesis]
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• The tensor bi-spectrum in a matter bounce
• The Integrated Bispectrum and Beyond
• The full CMB temperature bispectrum from single-field inflation
• Future CMB ISW-Lensing bispectrum constraints on modified gravity in the Parameterized Post-Friedmann formalism
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• Removing the ISW-lensing bias from the local-form primordial non-Gaussianity estimation
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• A Quantitative Central Limit Theorem for the Excursion Area of Random Spherical Harmonics over Subdomains of ${\mathbb{S}}^2$
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• The parity-odd Intrinsic Bispectrum
• A Consistency Relation for the CMB B-mode Polarization in the Squeezed Limit
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