A Minkowski Functional Analysis of the Cosmic Microwave Background Weak Lensing Convergence

Abstract

Minkowski functionals are summary statistics that capture the geometric and morphological properties of fields. They are sensitive to all higher order correlations of the fields and can be used to complement more conventional statistics, such as the power spectrum of the field. We develop a Minkowski functional-based approach for a full likelihood analysis of mildly non-Gaussian sky maps with partial sky coverage. Applying this to the inference of cosmological parameters from the Planck mission's map of the Cosmic Microwave Background's lensing convergence, we find an excellent agreement with results from the power spectrum-based lensing likelihood. While the non-Gaussianity of current CMB lensing maps is dominated by reconstruction noise, a Minkowski functional-based analysis may be able to extract cosmological information from the non-Gaussianity of future lensing maps and thus go beyond what is accessible with a power spectrum-based analysis. We make the numerical code for the calculation of a map's Minkowski functionals, skewness and kurtosis parameters available for download from GitHub.

23 pages, 15 figures

References in corpus (41)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Efficient Computation of CMB anisotropies in closed FRW models
• Weak Gravitational Lensing
• The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes
• Planck 2018 results. I. Overview and the cosmological legacy of Planck
• Dark Energy Survey Year 3 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing
• Weak Gravitational Lensing of the CMB
• Cosmology and Fundamental Physics with the Euclid Satellite
• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• Planck 2018 results. VIII. Gravitational lensing
• Cobaya: Code for Bayesian Analysis of hierarchical physical models
• Planck 2018 results. VII. Isotropy and Statistics of the CMB
• CMB-S4 Science Case, Reference Design, and Project Plan
• Planck 2018 results. III. High Frequency Instrument data processing and frequency maps
• Minkowski Functionals used in the Morphological Analysis of Cosmic Microwave Background Anisotropy Maps
• The power spectrum and bispectrum of SDSS DR11 BOSS galaxies I: bias and gravity
• Fast likelihood-free cosmology with neural density estimators and active learning
• Spherical Needlets for CMB Data Analysis
• Testing for Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe Data: Minkowski Functionals and the Length of the Skeleton
• Cosmology Constraints from the Weak Lensing Peak Counts and the Power Spectrum in CFHTLenS
• Full-sky Gravitational Lensing Simulation for Large-area Galaxy Surveys and Cosmic Microwave Background Experiments
• Primordial Non-Gaussianity and Analytical Formula for Minkowski Functionals of the Cosmic Microwave Background and Large-scale Structure
• Likelihood-free inference with neural compression of DES SV weak lensing map statistics
• Emulating the CFHTLenS Weak Lensing data: Cosmological Constraints from moments and Minkowski functionals
• Minkowski Functionals of SDSS galaxies I : Analysis of Excursion Sets
• Maximum a posteriori CMB lensing reconstruction
• Analytic Minkowski Functionals of the Cosmic Microwave Background: Second-order Non-Gaussianity with Bispectrum and Trispectrum
• Non Gaussianity and Minkowski Functionals: forecasts for Planck
• Cosmological Forecast for non-Gaussian Statistics in large-scale weak Lensing Surveys
• Constraining neutrino mass with weak lensing Minkowski Functionals
• Full-sky maps for gravitational lensing of the CMB
• CMB Lensing Beyond the Power Spectrum: Cosmological Constraints from the One-Point PDF and Peak Counts
• Going deep with Minkowski functionals of convergence maps
• Model-independent analyses of non-Gaussianity in Planck CMB maps using Minkowski Functionals
• Minkowski Functionals of SDSS-III BOSS : Hints of Possible Anisotropy in the Density Field?
• Local analyses of Planck maps with Minkowski Functionals
• Probing massive neutrinos with the Minkowski functionals of large-scale structure
• Minkowski Functionals of CMB polarisation intensity with Pynkowski: theory and application to Planck and future data
• Morphometric analysis in gamma-ray astronomy using Minkowski functionals - Source detection via structure quantification
• On the Limiting Behaviour of Needlets Polyspectra
• Tomographic local 2D analyses of the WISExSuperCOSMOS all-sky galaxy catalogue

Cited by in corpus (2)

• Cosmological constraints using Minkowski functionals from the first year data of the Hyper Suprime-Cam
• Morphometry on the sphere: Cartesian and irreducible Minkowski tensors explained and implemented