A like-for-like framework for persistent homology on galaxy surveys, and a topological anomaly in DESI BGS

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ID: 328510
2026
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Abstract
Abstract We apply three-dimensional persistent homology (PH) to the observed DESI Bright Galaxy Survey DR1 galaxy field (NGC; 217,614 galaxies, z ∈ [0.1, 0.4]) and show that naive PH comparisons between a bounded survey and periodic-box mocks are dominated by two systematics that can masquerade as physical anomalies. First, the mean H1 persistence depends on the dimensionless smoothing parameter σpx = R/Δx, not on the physical scale R alone (+8.42σ between σpx = 0.216 and 0.640), invalidating cross-survey comparisons at fixed R. Second, embedding a masked survey in a zero-padded cube with an unmasked filtration produces boundary-driven features — high mean persistence with a suppressed generator count — that are largely persistence-diagram truncation, not cosmology. We introduce a like-for-like framework (cut-sky mocks matched in footprint, selection, redshift-space distortions, density, weighting, and σpx, with a masked filtration) and apply it to DESI BGS against 2000 Quijote w0CDM cosmologies. Most of the apparent signal dissolves. One feature survives: the DESI field contains fewer H1 generators than all 2000 mocks (rank 1/2001; look-elsewhere bound p < 8/2001), robust to an HOD refit and more concentrated occupations, to weighting, to an angular fiber-incompleteness surrogate, and to a ±20% variation of the satellite velocity dispersion. The in-range w0 response is flat, so no sampled w0 reproduces it. We report this deficit as an open anomaly, not a dark-energy detection, and release the pipeline as a template for PH analyses of observed galaxy fields.
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Authors A. Marconi
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Journal monthly notices of the royal astronomical society
Year 2026
DOI
10.1093/mnras/stag1730
URL
https://academic.oup.com/mnras/advance-article-pdf/doi/10.1093/mnras/stag1730/71034180/stag1730.pdf
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