Principal components of CMB non-Gaussianity

Abstract

The skew-spectrum statistic introduced by Munshi & Heavens has recently been used in studies of non-Gaussianity from diverse cosmological data sets including the detection of primary and secondary non-Gaussianity of cosmic microwave background (CMB) radiation. Extending previous work, focused on independent estimation, here we deal with the question of joint estimation of multiple skew-spectra from the same or correlated data sets. We consider the optimum skew-spectra for various models of primordial non-Gaussianity as well as secondary bispectra that originate from the cross-correlation of secondaries and lensing of CMB: coupling of lensing with the Integrated Sachs–Wolfe effect, coupling of lensing with thermal Sunyaev–Zeldovich, as well as from unresolved point sources. For joint estimation of various types of non-Gaussianity, we use the principal component analysis (PCA) to construct the linear combinations of amplitudes of various models of non-Gaussianity, e.g. |$f^{\rm loc}_{\rm NL},f^{\rm eq}_{\rm NL},f^{\rm ortho}_{\rm NL}$| that can be estimated from CMB maps. We describe how the bias induced in the estimation of primordial non-Gaussianity due to secondary non-Gaussianity may be evaluated for arbitrary primordial models using a PCA analysis. The PCA approach allows one to infer approximate (but generally accurate) constraints using CMB data sets on any reasonably smooth model by use of a look-up table and performing a simple computation. This principle is validated by computing constraints on the Dirac–Born–Infeld bispectrum using a PCA analysis of the standard templates.