Analytic Minkowski Functionals of the Cosmic Microwave Background: Second-order Non-Gaussianity with Bispectrum and Trispectrum

TL;DR

This paper derives analytical formulas for Minkowski functionals of the CMB, incorporating second-order non-Gaussian effects from bispectrum and trispectrum, aiding in constraining primordial non-Gaussianity.

Contribution

It provides the first comprehensive analytical framework for Minkowski functionals including second-order non-Gaussianity from both bispectrum and trispectrum, applicable to various models.

Findings

Analytical formulas match numerical simulations well.

Formulas explicitly relate Minkowski functionals to non-Gaussian parameters.

Applicable to a broad class of non-Gaussian models.

Abstract

Analytic formulas of Minkowski functionals in two-dimensional random fields are derived, including effects of second-order non-Gaussianity in the presence of both the bispectrum and trispectrum. The set of formulas provides a promising method to constrain the primordial non-Gaussianity of the universe by temperature fluctuations in the cosmic microwave background radiation. In a case of local-type non-Gaussianity, the Minkowski functionals are analytically given by powers of quadratic and cubic parameters, $f_{\rm NL}$ and $g_{\rm NL}$. Our formulas are not restricted to this particular model, and applicable to a wide class of non-Gaussian models. The analytic formulas are compared to numerical evaluations from non-Gaussian realizations of temperature maps, showing very good agreements.