Cosmological Applications of the Gaussian Kinematic Formula

TL;DR

This paper applies the Gaussian Kinematic Formula to cosmological data, specifically CMB fields, enabling precise predictions of Minkowski functionals on masked, non-Gaussian spherical maps, validated by simulations.

Contribution

It extends the GKF application to multipoles and needlet components of CMB data, improving cosmic variance control and analysis in harmonic and real domains.

Findings

Theoretical predictions match Monte Carlo simulations perfectly.

GKF provides explicit expected values for Minkowski functionals on masked, non-Gaussian maps.

Method enhances analysis of CMB data by incorporating sky masks and non-Gaussian features.

Abstract

The Gaussian Kinematic Formula (GKF, see Adler and Taylor (2007,2011)) is an extremely powerful tool allowing for explicit analytic predictions of expected values of Minkowski functionals under realistic experimental conditions for cosmological data collections. In this paper, we implement Minkowski functionals on multipoles and needlet components of CMB fields, thus allowing a better control of cosmic variance and extraction of information on both harmonic and real domains; we then exploit the GKF to provide their expected values on spherical maps, in the presence of arbitrary sky masks, and under nonGaussian circumstances. All our results are validated by numerical experiments, which show a perfect agreement between theoretical predictions and Monte Carlo simulations.