Testing Statistical Isotropy on the Sphere with Minkowski Tensors

arXiv:2607.23973 · astro-ph.CO · Submitted 2026-07-27 · Read on arXiv

Stephen Appleby, Changbom Park

astro-ph.CO

Submitted: 2026-07-27

Comments: Comments welcome!

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Alignment — 43× in this paper · explained in 1 episode
• Anisotropy — 37× in this paper · explained in 3 episodes
• Trace — 14× in this paper · explained in 2 episodes
• Gravitational Lensing — 5× in this paper · explained in 2 episodes
• Non-Gaussianity — 5× in this paper · explained in 2 episodes
• Weak Lensing — 5× in this paper · explained in 2 episodes
• Korea Institute for Advanced Study — 2× in this paper
• Persistent Homology — 2× in this paper · explained in 3 episodes
• Point Clouds — 2× in this paper · explained in 2 episodes
• alpha — 2× in this paper · explained in 1 episode
• Clustering — 1× in this paper · explained in 2 episodes
• Non-stationarity — 1× in this paper · explained in 2 episodes
• Primordial non-Gaussianity — 1× in this paper · explained in 2 episodes
• Simulation-based Inference — 1× in this paper · explained in 2 episodes
• Symmetry Breaking — 1× in this paper · explained in 3 episodes

Sources

• Is the Observable Universe Consistent with the Cosmological Principle?
• Planck 2018 results. VII. Isotropy and Statistics of the CMB
• A Test of the Cosmological Principle with Quasars
• Power Asymmetry in Cosmic Microwave Background Fluctuations from Full Sky to Sub-degree Scales: Is the Universe Isotropic?
• Cosmic radio dipole from NVSS and WENSS
• Strong Evidence Against a Statistically Isotropic Universe
• How isotropic is dark energy?
• Planck 2018 results. VI. Cosmological parameters
• A large disparity in cosmic reference frames determined from the sky distributions of radio sources and the microwave background radiation
• Integrated perturbation theory for cosmological tensor fields. I. Basic formulation
• Integrated perturbation theory for cosmological tensor fields. II. Loop corrections
• Integrated perturbation theory for cosmological tensor fields. III. Projection effects
• Integrated perturbation theory for cosmological tensor fields. IV. Full-sky formulation
• Information content in anisotropic cosmological fields: Impact of different multipole expansion scheme for galaxy density and ellipticity correlations
• Limits on Primordial Non-Gaussianity from Minkowski Functionals of the WMAP Temperature Anisotropies
• Local analyses of Planck maps with Minkowski Functionals
• On Minkowski Functionals of CMB polarization
• Minkowski Functionals of SDSS-III BOSS : Hints of Possible Anisotropy in the Density Field?
• Betti numbers of Gaussian fields
• Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web

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