The Pursuit of Non-Gaussian Fluctuations in the Cosmic Microwave Background
Eiichiro Komatsu
TL;DR
The paper develops a comprehensive framework to detect and characterize non-Gaussian fluctuations in the CMB via angular bispectrum and trispectrum analyses. It provides theoretical predictions for a primary non-Gaussian signal from slow-roll inflation (parameterized by $f_{ m NL}$) and for secondary/foreground bispectra, and couples these with practical estimators and Fisher-matrix methods to assess measurability. Applying these methods to COBE DMR data, the study finds no significant non-Gaussianity, placing weak constraints on inflationary non-linearity and foreground contributions; the results nonetheless establish a powerful, shape-sensitive approach for future MAP/Planck analyses. The trispectrum analysis further tests Gaussianity and demonstrates the potential of higher-order statistics to probe non-Gaussianity from lensing and cosmic topology, with implications for power spectrum covariance and cosmological parameter estimation. Overall, the angular bispectrum and trispectrum emerge as robust, model-driven tools for testing inflationary physics and low-redshift astrophysical processes with upcoming high-sensitivity CMB data.
Abstract
We present theoretical and observational studies of non-Gaussian fluctuations in CMB, by using the angular bispectrum and trispectrum. We predict the primary angular bispectrum from inflation, and forecast how well we can measure the primordial non-Gaussian signal. In addition to that, secondary anisotropy sources in the low-redshift universe also produce non-Gaussianity, so do foreground emissions from extragalactic or interstellar microwave sources. We study how well we can measure these non-Gaussian signals, including the primordial signal. We find that slow-roll inflation produces too small bispectrum to be detected by any experiments; thus, any detection strongly constrains this class of models. We also find that the secondary bispectrum from coupling between the SZ effect and the weak lensing effect, and the foreground bispectrum from extragalactic point sources, give detectable non-Gaussian signals on small angular scales. We test Gaussianity of the COBE DMR sky maps, by measuring all the modes of the angular bispectrum down to the DMR beam size. We find no significant signal of the bispectrum. We also find that the previously reported detection of the bispectrum is consistent with a statistical fluctuation. By fitting the theoretical prediction to the data for the primary bispectrum, we put a constraint on non-linearity in inflation. We conclude that the angular bispectrum finds no significant non-Gaussian signals in the DMR data. We present the first measurement of the angular trispectrum on the DMR sky maps, further testing Gaussianity of the DMR data. We find no significant non-Gaussian signals in the trispectrum. Therefore, the angular bispectrum and trispectrum show that the DMR sky map is comfortably consistent with Gaussianity.