The Cosmological Correlation Dimension Beyond the Linear Regime: Analytical Approximation and Parameter Sensitivity

arXiv:2609.39867 · astro-ph.CO · Submitted 2026-09-30 · Read on arXiv

astro-ph.CO

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Homogeneity — 23× in this paper · explained in 2 episodes
• Clustering — 16× in this paper · explained in 2 episodes
• Matter Power Spectrum — 14× in this paper · explained in 2 episodes
• Calibration — 8× in this paper · explained in 7 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Consistency — 3× in this paper · explained in 3 episodes
• Degeneracy — 3× in this paper · explained in 3 episodes
• Objective Function — 3× in this paper · explained in 2 episodes
• Principal Component — 3× in this paper
• Robustness — 2× in this paper · explained in 5 episodes
• Anti-correlation — 1× in this paper · explained in 3 episodes
• Model-Agnostic — 1× in this paper · explained in 2 episodes
• N-body simulations — 1× in this paper · explained in 2 episodes
• Polynomial Chaos Expansion — 1× in this paper
• Redundancy — 1× in this paper · explained in 2 episodes
• Velocity Dispersion — 1× in this paper · explained in 2 episodes

Sources

• Scaling in the Universe
• The Fractal Geometry of the Cosmic Web and its Formation
• Fractal Dimension as a measure of the scale of Homogeneity
• Correlation function: biasing and fractal properties of the cosmic web
• Cosmic homogeneity demonstrated with luminous red galaxies
• The WiggleZ Dark Energy Survey: the transition to large-scale cosmic homogeneity
• Investigating Cosmic Homogeneity Using Multi-fractal Analysis of the SDSS-IV eBOSS DR16 Quasar Catalog
• Accelerating Universes with Scaling Dark Matter
• Exploring the Expansion History of the Universe
• An accurate halo model for fitting non-linear cosmological power spectra and baryonic feedback models
• HMcode-2020: Improved modelling of non-linear cosmological power spectra with baryonic feedback
• Euclid preparation: II. The EuclidEmulator -- A tool to compute the cosmology dependence of the nonlinear matter power spectrum
• Euclid preparation: IX. EuclidEmulator2 -- Power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations
• 4D Gravity on a Brane in 5D Minkowski Space
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Non-linear evolution of f(R) cosmologies II: power spectrum
• Modified Gravity N-body Code Comparison Project
• On the road to percent accuracy: nonlinear reaction of the matter power spectrum to dark energy and modified gravity
• Exploring cosmic homogeneity with the BOSS DR12 galaxy sample
• The scale of cosmic homogeneity as a standard ruler

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