The CMB bispectrum

We use a separable mode expansion estimator with WMAP7 data to estimate the bispectrum for all the primary families of non-Gaussian models, including non-scaling feature (periodic) models, the flat (trans-Planckian) model, DBI and ghost inflation, as well as previously constrained simple cases. We review the late-time mode expansion estimator methodology which can be applied to any non-separable primordial and CMB bispectrum model, and we demonstrate how the method can be used to reconstruct the CMB bispectrum from an observational map. We extend the previous validation of the general estimator using local map simulations. We apply the estimator to the coadded WMAP 7-year V and W channel maps, reconstructing the WMAP bispectrum using l < 500 multipoles and n = 50 orthonormal 3D eigenmodes; both the mode expansion parameters and the reconstructed 3D WMAP bispectrum are plotted. We constrain all popular nearly scale-invariant models, ensuring that the theoretical bispectrum is well-described by a convergent mode expansion. Constraints from the local model f(NL), = 20.31 +/- 27.64 and the equilateral model f(NL), = 10.19 +/- 127.38 (F-NL = 1.90 +/- 23.79) are consistent with previously published results. (Here, we use a nonlinearity parameter F-NL normalised to the local case, to allow more direct comparison between different models.) Notable new constraints from our method include those for the constant model F-NL = 7.82 +/- 24.57, the flat model F-NL = 7.31 +/- 26.22, and warm inflation F-NL = 2.10 +/- 25.83. We investigate feature models, which break scale invariance, surveying a wide parameter range for both the scale and phase (scanning for feature models with an effective period l* > 150). We find no significant evidence of non-Gaussianity for all cases well-described by the given eigenmodes. In the overall non-Gaussian analysis, we find one anomalous mode n = 33 with a 3.39 sigma amplitude which could give rise to an oscillatory model signal with l* <= 150. We propose a measure (F) over bar (NL) for the total integrated bispectrum and find that the measured value is consistent with the null hypothesis that CMB anisotropies obey Gaussian statistics. We argue that this general bispectrum survey with the WMAP data represents the best test of Gaussianity to date and we discuss future prospects with higher precision and resolution, notably from the Planck satellite.