CMB contraints on primordial non-Gaussianity from the bispectrum (fNL) and trispectrum (gNL and τNL) and a new consistency test of single-field inflation

We outline the expected constraints on non-Gaussianity from the cosmic microwave background with current and future experiments, focusing on both the third (f_NL) and fourth-order (g_NL and τ_NL) amplitudes of the local configuration or non-Gaussianity. The experimental focus is the skewness (two-to-one) and kurtosis (two-to-two and three-to-one) power spectra from weighted maps. In addition to a measurement of τ_NL and g_NL with WMAP 5-year data, our study provides the first forecasts for future constraints on g_NL. We describe how these statistics can be corrected for the mask and cut-sky through a window function, bypassing the need to compute linear terms that were introduced for the previous-generation non-Gaussianity statistics, such as the skewness estimator. We discus the ratio A_NL=τ_NL/(6f_NL/5)² as an additional test of single-field inflationary models and discuss the physical significance of each statistic. Using these estimators with WMAP 5-Year V+W-band data out to l_max⁡=600 we constrain the cubic order non-Gaussianity parameters τ_NL, and g_NL and find -7.4<g_NL/10⁵<8.2 and -0.6<τ_NL/10⁴<3.3 improving the previous COBE-based limit on τ_NL<10⁸ nearly 4 orders of magnitude with WMAP.