Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations

Abstract

We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non- Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to 7σ for fNL values (both true and sampled) not ruled out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.

Matches accepted verion to JCAP; conclusions unchaged, extra references added

References in corpus (7)

• Primordial Non-Gaussianities from Inflation Models
• Effects of Scale-Dependent Non-Gaussianity on Cosmological Structures
• 21-cm Background Anisotropies Can Discern Primordial Non-Gaussianity
• The bispectrum of redshifted 21-cm fluctuations from the dark ages
• The CMB Bispectrum, Trispectrum, non-Gaussianity, and the Cramer-Rao Bound
• Local non-Gaussianity in the Cosmic Microwave Background the Bayesian way
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Cited by in corpus (9)

• Planck 2018 results. X. Constraints on inflation
• Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity
• The power spectrum and bispectrum of SDSS DR11 BOSS galaxies I: bias and gravity
• Hunting high and low: Disentangling primordial and late-time non-Gaussianity with cosmic densities in spheres
• Non-Gaussianity of secondary anisotropies from ACTPol and Planck
• Generic inference of inflation models by non-Gaussianity and primordial power spectrum reconstruction
• The bias of weighted dark matter halos from peak theory
• Non-Gaussian CMB and LSS statistics beyond polyspectra
• Fast and precise way to calculate the posterior for the local non-Gaussianity parameter $f_{\text{nl}}$ from cosmic microwave background observations