A First Detection of the Connected 4-Point Correlation Function of Galaxies Using the BOSS CMASS Sample

2021/08/03 by Oliver H. E. Philcox, Jiamin Hou, Philcox, Oliver H. E. +3 · 24 citations
Mathematics · Physics and Astronomy · #Algorithm #Approx #Astronomy and Astrophysical Research #Astrophysics #Astrophysics of Galaxies (astro-ph.GA) #Computer science #Correlation function (quantum field theory) #Cosmology and Gravitation Theories #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #Covariance #Estimator #FOS: Physical sciences #Galaxies: Formation, Evolution, Phenomena #Galaxy #Gaussian #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Experiment (hep-ex) #High Energy Physics - Phenomenology (hep-ph) #Mathematics #Physics #Spectral density #Statistical physics #Statistics #astro-ph.CO #astro-ph.GA #gr-qc #hep-ex #hep-ph

paper · pdf · doi:10.48550/arxiv.2108.01670

published in arXiv (Cornell University) (Cornell University) · 26 pages, 9 figures, submitted to Phys. Rev. D. Code available at https://github.com/oliverphilcox/Parity-Even-4PCF

arxiv created 2021/08/03 · openalex publication_date 2021/08/03 · arxiv updated 2021/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an 8.1σ detection of the non-Gaussian 4-Point Correlation Function (4PCF) using a sample of N_{\rm g} ≈ 8× 10⁵ galaxies from the BOSS CMASS dataset. Our measurement uses the O(N_{\rm g}²) NPCF estimator of Philcox et al. (2021), including a new modification to subtract the disconnected 4PCF contribution (arising from the product of two 2PCFs) at the estimator level. This approach is unlike previous work and ensures that our signal is a robust detection of gravitationally-induced non-Gaussianity. The estimator is validated with a suite of lognormal simulations, and the analytic form of the disconnected contribution is discussed. Due to the high dimensionality of the 4PCF, data compression is required; we use a signal-to-noise-based scheme calibrated from theoretical covariance matrices to restrict to ∼ 100 basis vectors. The compression has minimal impact on the detection significance and facilitates traditional χ²-like analyses using a suite of mock catalogs. The significance is stable with respect to different treatments of noise in the sample covariance (arising from the limited number of mocks), but decreases to 4.7σ when a minimum galaxy separation of 14 h^-1Mpc is enforced on the 4PCF tetrahedra (such that the statistic can be modelled more easily). The detectability of the 4PCF in the quasi-linear regime implies that it will become a useful tool in constraining cosmological and galaxy formation parameters from upcoming spectroscopic surveys.

Citations

• Fast n-point correlation functions and three-point lensing application
• The Approximation of One Matrix by Another of Lower Rank
• Non-Gaussianity from Inflation: Theory and Observations
• Modeling the Galaxy Three‐Point Correlation Function
• Improving the Line of Sight for the Anisotropic 3-Point Correlation Function of Galaxies: Centroid and Unit-Vector-Average Methods Scaling as O(N²)

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• Four-point correlation functions in axion inflation
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• Analytic Model for Covariance Matrices of the 2-, 3-, and 4-Point Correlation Functions in the Gaussian Random Field Approximation

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