Three-point temperature anisotropies in WMAP: Limits on CMB non-Gaussianities and nonlinearities

We present a study of the three-point angular correlation function w₃=〈δ₁δ₂δ₃〉 of (adimensional) temperature anisotropies measured by the Wilkinson Microwave Anisotropy Probe. The results can be normalized to the two-point function w₂=〈δ₁δ₂〉 in terms of the hierarchical q₃~w₃/w₂² or dimensionless d₃~w₃/w₂3/2 amplitudes. Strongly non-Gaussian models are generically expected to show d₃>1 or q₃>10³d₃. Unfortunately, this is comparable to the cosmic variance on large angular scales. For Gaussian primordial models, q₃ gives a direct measure of the nonlinear corrections to temperature anisotropies in the sky: δ=δL+fNLT(δL²-〈δL²〉) with fNLT=q₃/2 for the leading order term in w₂². We find good agreement with the Gaussian hypothesis d₃~0 within the cosmic variance of the simulations of the cold dark matter model with a cosmological constant (ΛCDM) (with or without a low quadrupole). The strongest constraints on q₃ come from scales smaller than 1^∘. We find q₃=19±141 for (pseudo) collapsed configurations and an average of q₃=336±218 for noncollapsed triangles. The corresponding nonlinear coupling parameter fNL for curvature perturbations Φ, in the Sachs-Wolfe regime is fNLSW=q₃/6, while on degree scales, the extra power in acoustic oscillations produces fNL~q₃/30 in the ΛCDM. Errors are dominated by cosmic variance, but for the first time they begin to be small enough to constrain the leading order nonlinear effects with a coupling of the order of unity.