Review Article
Primordial Non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure
Table 3
Constraints on ,, obtained by different groups on the one-year (W1), three-year (W3), five-year (W5), and seven-year (W7) WMAP data releases. Different rows correspond to the different implementations of the estimator described in the text: the “pure cubic” implementation (100) in which no linear term is included, the “pseudooptimal” implementation (114) in which a linear term is added but the covariance matrix is assumed to be diagonal in the cubic term, and the fully “optimal” implementation (98). As we noted in the text, the linear term is important mostly for estimates of local NG, since anisotropic noise “mimics” squeezed configuration. For this reason “pure cubic” estimates of equilateral NG in the table are nearly optimal, while local ones are significantly suboptimal, especially because they have to be confined to the pure signal-dominated region , where the assumption of rotational invariance is correct. There is a certain degree of friction between some of the results shown. In particular the WMAP 3-year estimate obtained by Yadav and Wandelt in [79], corresponding to a “nearly 3-” detection of local NG, seems not to agree well with the , result obtained on the same dataset by Smith et al. in [68]. The origin of the discrepancy is unclear, although it is argued by Smith et al. in [68] that it might be due to differences in the coadding scheme of different data channels, or analogous differences in the choice of some weights. As pointed out in Smith et al. [68], one additional advantage of the fully optimal implementation of the estimator is actually that all of the ambiguity related to the use of different coadding schemes disappears, since the optimal coadding strategy is automatically selected in the inverse covariance filtering process. Another discrepancy is that between the two equilateral constraints on WMAP 5-year data. It seems that the pseudooptimal estimator produces better constraints than the optimal one. This is clearly not possible. Smith et al. [68] claim that their numerical pipeline calculates the theoretical ansatz for the bispectrum shape more accurately than it was done before. That is due to a subtlety that went unnoticed in previous works, consisting in the necessity to extend above the horizon the upper integration limit in the calculation of the equilateral shape-related quantities , , and (see (55)). This is required in order to obtain stable numerical solutions, and it calls for a reassessment of the expected and measured error bars, which actually increase with respect to previous calculations.