Cosmic microwave background bispectrum from nonlinear effects during recombination

Abstract

We study cosmological perturbations by solving the governing Boltzmann and Einstein field equations up to second order and calculate the corresponding CMB bispectrum during recombination. We include all the second-order Liouville and collision terms, truncating the multipole hierarchy at $l=10$, consistently including all $m\ensuremath{\ne}0$ terms when calculating the bispectrum in the flat-sky limit. At this stage, we focus on contributions at and around recombination, and we neglect second-order vector and tensor perturbations, lensing effects, and late-time nonlinear ISW effects. We find that the signal-to-noise for the bispectrum is 0.69 for ${l}_{\mathrm{max}}=2000$, yielding an overall signal ${F}_{\mathrm{NL}}=3.19$ (normalized relative to the local model). We find that the effective ${f}_{\mathrm{NL}}$'s of the equilateral and local type are 5.11 and 0.88, respectively. This recombination signal will have to be taken into account in a quantitative analysis of the Planck data.