Applications of the Gaussian kinematic formula to CMB data analysis

The Gaussian kinematic formula (GKF) [R.J. Adler and J.E. Taylor, Random Fields and Geometry (Springer, New York, 2007).] 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 non-Gaussian circumstances. All our results are validated by numerical experiments, which show a perfect agreement between theoretical predictions and Monte Carlo simulations.