Cosmic microwave background bispectrum on small angular scales

This article investigates the nonlinear evolution of cosmological perturbations on sub-Hubble scales in order to evaluate the unavoidable deviations from Gaussianity that arise from the nonlinear dynamics. It shows that the dominant contribution to modes coupling in the cosmic microwave background temperature anisotropies on small angular scales is driven by the sub-Hubble nonlinear evolution of the dark matter component. The perturbation equations, involving, in particular, the first moments of the Boltzmann equation for photons, are integrated up to second order in perturbations. An analytical analysis of the solutions gives a physical understanding of the result as well as an estimation of its order of magnitude. This allows one to quantify the expected deviation from Gaussianity of the cosmic microwave background temperature anisotropy and, in particular, to compute its bispectrum on small angular scales. Restricting to equilateral configurations, we show that the nonlinear evolution accounts for a contribution that would be equivalent to a constant primordial non-Gaussianity of order fNL∼25 on scales ranging approximately from ∼1000 to ∼3000.