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 tau(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 tau(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) = tau(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 tau(NL), and g(NL) and find -7.4 < g(NL)/10(5) < 8.2 and -0.6 < tau(NL)/10(4) < 3.3 improving the previous COBE-based limit on tau(NL) < 10(8) nearly 4 orders of magnitude with WMAP.