Sachs-Wolfe at second order: the CMB bispectrum on large angular scales

Lotfi Boubekeur, Paolo Creminelli, Guido D'Amico, Jorge Noreña, Filippo Vernizzi

Published 2009-06-04, updated 2009-09-16Version 2

We calculate the Cosmic Microwave Background anisotropy bispectrum on large angular scales in the absence of primordial non-Gaussianities, assuming exact matter dominance and extending at second order the classic Sachs-Wolfe result \delta T/T=\Phi/3. The calculation is done in Poisson gauge. Besides intrinsic contributions calculated at last scattering, one must consider integrated effects. These are associated to lensing, and to the time dependence of the potentials (Rees-Sciama) and of the vector and tensor components of the metric generated at second order. The bispectrum is explicitly computed in the flat-sky approximation. It scales as l^(-4) in the scale invariant limit and the shape dependence of its various contributions is represented in 3d plots. Although all the contributions to the bispectrum are parametrically of the same order, the full bispectrum is dominated by lensing. In the squeezed limit it corresponds to f_NL^local = -1/6 - cos(2 \theta), where \theta is the angle between the short and the long modes; the angle dependent contribution comes from lensing. In the equilateral limit it corresponds to f_NL^equil ~ 3.13.