The full squeezed CMB bispectrum from inflation

Lewis, Antony (2012) The full squeezed CMB bispectrum from inflation. Journal of Cosmology and Astroparticle Physics, 23 (6). pp. 1-20. ISSN 1475-7516

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Subjects: Q Science > QB Astronomy > QB0980 Cosmogony. Cosmology
Depositing User: Antony Lewis
Date Deposited: 07 Nov 2012 14:47
Last Modified: 03 Dec 2012 13:09
URI: http://sro.sussex.ac.uk/id/eprint/41383
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