3-point temperature anisotropies in WMAP: Limits on CMB non-Gaussianities and non-linearities

Abstract

We present a study of the 3-pt angular correlation function w_3= <delta_1 delta_2 delta_3> of (adimensional) temperature anisotropies measured by the Wilkinson Microwave Anisotropy Probe (WMAP). Results can be normalized to the 2-point function w_2 = <delta_1 delta_2> in terms of the hierarchical: q_3 ~ w_3/w_2^2 or dimensionless: d_3 ~ w_2/w_2^{3/2}$ amplitudes. Strongly non-Gaussian models are generically expected to show d_3 > 1 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 non-linear corrections to temperature anisotropies in the sky: delta = delta_L + f_{NLT} (delta_L^2 - <delta_L^2>) with f_{NLT} = q_3/2 for the leading order term in w_2^2. We find good agreement with the Gaussian hypothesis d_3 ~ 0 within the cosmic variance of LCDM simulations (with or without a low quadrupole). The strongest constraints on q_3 come from scales smaller than 1 degree. We find q_3 =19 +/-141 for (pseudo) collapsed configurations and an average of q_3 = 336 +/-218 for non-collapsed triangles. The corresponding non-linear coupling parameter, f_{NL}, for curvature perturbations Phi, in the Sachs-Wolfe (SW) regime is: f_{NL}^{SW} = q_3/6, while on degree scales, the extra power in acoustic oscillations produces f_{NL} ~ q_3/30 in the LCM model. Errors are dominated by cosmic variance, but for the first time they begin to be small enough to constrain the leading order non-linear effects with coupling of order unity.