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

Abstract

We present a study of the three-point angular correlation function ${w}_{3}=〈{\ensuremath{\delta}}_{1}{\ensuremath{\delta}}_{2}{\ensuremath{\delta}}_{3}〉$ of (adimensional) temperature anisotropies measured by the Wilkinson Microwave Anisotropy Probe. The results can be normalized to the two-point function ${w}_{2}=〈{\ensuremath{\delta}}_{1}{\ensuremath{\delta}}_{2}〉$ in terms of the hierarchical ${q}_{3}\ensuremath{\sim}{w}_{3}{/w}_{2}^{2}$ or dimensionless ${d}_{3}\ensuremath{\sim}{w}_{3}{/w}_{2}^{3/2}$ amplitudes. Strongly non-Gaussian models are generically expected to show ${d}_{3}g1$ or ${q}_{3}g{10}^{3}{d}_{3}.$ 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: $\ensuremath{\delta}={\ensuremath{\delta}}_{L}{+f}_{\mathrm{NLT}}({\ensuremath{\delta}}_{L}^{2}\ensuremath{-}〈{\ensuremath{\delta}}_{L}^{2}〉)$ with ${f}_{\mathrm{NLT}}{=q}_{3}/2$ for the leading order term in ${w}_{2}^{2}.$ We find good agreement with the Gaussian hypothesis ${d}_{3}\ensuremath{\sim}0$ within the cosmic variance of the simulations of the cold dark matter model with a cosmological constant $(\ensuremath{\Lambda}\mathrm{CDM})$ (with or without a low quadrupole). The strongest constraints on ${q}_{3}$ come from scales smaller than $1\ifmmode^\circ\else\textdegree\fi{}.$ We find ${q}_{3}=19\ifmmode\pm\else\textpm\fi{}141$ for (pseudo) collapsed configurations and an average of ${q}_{3}=336\ifmmode\pm\else\textpm\fi{}218$ for noncollapsed triangles. The corresponding nonlinear coupling parameter ${f}_{\mathrm{NL}}$ for curvature perturbations $\ensuremath{\Phi},$ 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 ${f}_{\mathrm{NL}}\ensuremath{\sim}{q}_{3}/30$ in the $\ensuremath{\Lambda}\mathrm{CDM}.$ 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.