The integrated bispectrum as a test of cosmic microwave background non-Gaussianity: detection power and limits on f_NL with WMAP data

We propose a fast and efficient bispectrum statistic for cosmic microwave background (CMB) temperature anisotropies to constrain the amplitude of the primordial non-Gaussian signal measured in terms of the non-linear coupling parameter fNL. We show how the method can achieve a remarkable computational advantage by focusing on subsets of the multipole configurations, where the non-Gaussian signal is more concentrated. The detection power of the test increases roughly linearly with the maximum multipole, as shown in the ideal case of an experiment without noise and gaps. The CPU-time scales as l3max instead of l5max for the full bispectrum, which for Planck resolution lmax ~ 3000 means an improvement in speed of a factor of 107 compared with the full bispectrum analysis with minor loss in precision. This approach is complementary to the fast method introduced by Komatsu, Spergel & Wandelt using a reconstruction of the primordial fluctuation field. We find that the introduction of a galactic cut partially destroys the optimality of the configuration, which will then need to be dealt with in the future. We find for an ideal experiment with lmax = 2000 that upper limits of fNL < 8 can be obtained at 1σ. For the case of the WMAP experiment, we would be able to put limits of |fNL| < 40 if no galactic cut were present. Using the real data with a galactic cut, we obtain an estimate of -80 < fNL < 80 and -160 < fNL < 160 at 1 and 2σ, respectively.