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

We present a study of the three-point angular correlation function $w_3=〈{\delta }_1{\delta }_2{\delta }_3〉$ of (adimensional) temperature anisotropies measured by the Wilkinson Microwave Anisotropy Probe. The results can be normalized to the two-point function $w_2=〈{\delta }_1{\delta }_2〉$ in terms of the hierarchical $q_3\sim w_3{/w}_2^2$ or dimensionless $d_3\sim w_3{/w}_2^{3/2}$ amplitudes. Strongly non-Gaussian models are generically expected to show $d_3>1\mathrm{}$ or $q_3>{10}^3{d}_3.$ Unfortunately, this is comparable to the cosmic variance on large angular scales. For Gaussian primordial models, $q_3$ gives a direct measure of the nonlinear corrections to temperature anisotropies in the sky: $\delta ={\delta }_L{+f}_{\mathrm{NLT}}\left({\delta }_L^2-〈{\delta }_L^2〉\right)$ with $f_{\mathrm{NLT}}{=q}_3/2\mathrm{}$ for the leading order term in $w_2^2.$ We find good agreement with the Gaussian hypothesis $d_3\sim 0$ within the cosmic variance of the simulations of the cold dark matter model with a cosmological constant $\left(\Lambda \mathrm{CDM}\right)$ (with or without a low quadrupole). The strongest constraints on $q_3$ come from scales smaller than $1°.$ We find $q_3=19\mathrm{}\pm 141$ for (pseudo) collapsed configurations and an average of $q_3=336\mathrm{}\pm 218$ for noncollapsed triangles. The corresponding nonlinear coupling parameter $f_{\mathrm{NL}}$ for curvature perturbations $\Phi ,$ in the Sachs-Wolfe regime is $f_{\mathrm{NL}}^{\mathrm{SW}}{=q}_3/6,$ while on degree scales, the extra power in acoustic oscillations produces $f_{\mathrm{NL}}\sim q_3/30\mathrm{}$ in the