Cosmological Applications of the Gaussian Kinematic Formula

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.

19 pages, 10 figure panels

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Cited by in corpus (4)

• Minkowski Functionals of CMB polarisation intensity with Pynkowski: theory and application to Planck and future data
• Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the $\text{NPIPE}$ and $\text{FFP10}$ data releases
• Morphometry on the sphere: Cartesian and irreducible Minkowski tensors explained and implemented
• Asymptotic expansion of the expected Minkowski functional for isotropic central limit random fields