Large-Scale Galaxy Correlations from the DESI First Data Release

Published 26 Nov 2025 in astro-ph.CO | (2511.21585v1)

Abstract: We quantify galaxy correlations using two distinct three-dimensional samples from the first data release of the Dark Energy Spectroscopic Instrument (DESI): the Bright Galaxy Sample (BGS) and the Luminous Red Galaxy Sample (LRGS). Specifically, we measure the conditional average density, defined as the average density of galaxies observed around a typical galaxy in the sample. To minimize boundary effects, we adopt a conservative criterion: only galaxies for which a spherical volume of radius $r$, centered on them, is fully contained within the survey footprint are included in the computation. For the BGS, we construct four volume-limited subsamples in order to eliminate biases arising from luminosity-dependent selection effects. By contrast, the LRGS is approximately volume-limited by design. The resulting samples span different depths, providing an opportunity to test the stability of statistical measurements across survey volumes of increasing size. Our results show that the conditional average density follows a power-law decay, $\langle n(r) \rangle \propto r^{-0.8}$, without exhibiting any transition to homogeneity within the survey volume. The large statistics of the DESI samples also allow us to demonstrate that finite-size effects become significant as $r$ approaches the boundaries of the sample volumes. Consistently, we find that the distribution of density fluctuations follows a Gumbel distribution - characteristic of extreme-value statistics - rather than a Gaussian distribution, which would be expected for a spatially homogeneous field. These findings confirm and extend the trends previously observed in smaller redshift surveys, supporting the conclusion that the galaxy distribution does not undergo a transition to spatial homogeneity within the probed scales, up to $r \sim 400$~\text{Mpc}/$h$.

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Summary

The paper presents a conditional density analysis from DESI DR1, revealing that galaxy clustering follows a robust power-law decay without transitioning to homogeneity up to 400 Mpc/h.
It employs a methodology that minimizes selection bias through volume-limited subsamples and tailored angular masks to control systematic errors.
The results challenge standard CDM predictions by showing persistent inhomogeneity and non-Gaussian fluctuations, prompting reconsideration of large-scale structure models.

Large-Scale Galaxy Correlations in the DESI DR1: Absence of Homogeneity up to 400 Mpc/h

Introduction and Motivation

The statistical characterization of galaxy spatial distributions remains fundamental for cosmological inference, particularly regarding the scale of statistical homogeneity. The standard cosmological paradigm posits that the universe is well-described by a homogeneous and isotropic metric (FRW) at sufficiently large scales, and this underpins not only the background evolution but also most galaxy clustering analyses. However, the operational detection and characterization of the actual transition to homogeneity is intricate, confounded by selection effects and survey boundary conditions. The paper "Large-Scale Galaxy Correlations from the DESI First Data Release" (2511.21585) offers the first conditional density analysis of galaxy clustering in the DESI DR1 samples, targeting both Bright Galaxy Sample (BGS) and Luminous Red Galaxy Sample (LRGS), with special attention to methodology robust against luminosity selection bias and finite-volume artifacts.

Figure 1: DESI DR1 angular projection of the BGS and LRGS, showing the footprint and selected angular regions for conditional density analysis.

DESI DR1 Sample Construction, Selection, and Volume-Limited Subsamples

DESI DR1 represents the deepest and most extensive spectroscopic mapping to date, covering $\sim 14,000$ deg $^2$ and up to $>5$ million high-quality galaxy redshifts ($0.1 < z < 2.1$ for all four major target classes). The construction of subsamples for unbiased conditional density measurements is crucial. BGS subsamples are rendered volume-limited (VL) by imposing both distance and absolute magnitude cuts; LRGS is quasi-VL by survey design. The angular selection masks are engineered to maximize contiguous coverage and minimize selection function anisotropy. Completeness corrections are verified with random catalogs tailored to DESI selections.

Figure 2: Redshift and nearest-neighbor distributions for both BGS and LRGS, illustrating luminosity selection effects and the underlying clustering regime.

Figure 3: Projected spatial positions in Galactic coordinates for the R25 region across BGS VL subsamples, visually illustrating large-scale structure and sample depth.

Methodology: Conditional Density and Systematic Error Control

Unlike the two-point correlation function, which presumes a well-defined global mean density, the conditional average density $\langle n(r) \rangle$ quantifies the local average density in spheres of radius $r$ centered on galaxies, strictly requiring spheres to be fully embedded within the survey volume to avoid geometric bias. The mean, variance, and full PDF of $n_i(r)$ provide a comprehensive picture of clustering at each scale. Given the scale-dependence of the number of available centers, $C(r)$ , and volume overlaps $f_{\mathrm{overlap}}$ , the analysis explicitly tracks finite-size effects and the reliability of measured statistics.

Results: Conditional Density, Variance, and PDF of Fluctuations

Power-Law Decay and Persistence of Inhomogeneity

Across all BGS and LRGS subsamples, the conditional average density follows a robust power-law decay, $\langle n(r) \rangle \propto r^{-0.8}$ , without transition to uniformity up to the largest probed scales ( $r \sim 400$ Mpc/ $h$ ). The slope conjugates with nearest-neighbor statistics, indicating self-consistent clustering well beyond 100 Mpc/ $h$ .

Figure 4: Conditional average density $\langle n(r) \rangle$ versus $r$ for VL BGS and LRGS samples in different angular regions, showing persistent power-law decay.

Figure 5: Conditional density for LRGS in disjoint R25 subregions; $\sim$ 20% fluctuations highlight persistent spatial inhomogeneity at large scales.

Failure of Standard Cosmological Model Predictions

Comparison with linear CDM predictions for $\langle n(r) \rangle$ shows a stark discrepancy: CDM models produce a rapid transition to homogeneity ( $\gamma \to 0$ ) at $r \sim 80$ Mpc/ $h$ , not evidenced in the DESI data.

Figure 6: Conditional density predictions for CDM models, showing the rapid flattening absent in observational DESI samples.

Variance and Lack of Self-Averaging

Both the variance $\Sigma^2(r)$ and normalized variance $\Sigma(r)/\langle n(r) \rangle$ decay slower than the $r^{-3}$ expectation for a homogeneous Poissonian field, reflecting the persistence of large-scale fluctuations.

Figure 7: Variance $\Sigma^2(r)$ scaling for VL samples; shallow decay relative to expectation demonstrates extension of clustering.

Figure 8: Ratio $\Sigma(r)/\langle n(r) \rangle$ is of order unity or higher up to $r \sim 200$ Mpc/ $h$ , indicating a lack of self-averaging typical of non-homogeneous fields.

PDF Analysis: Gumbel vs Gaussian Fluctuation Statistics

The PDF of galaxy counts $P(N; r)$ within spheres of growing radius continues to be well-approximated by a Gumbel distribution, characteristic of systems governed by extreme-value statistics, not by a Gaussian distribution as would occur for a homogeneous random field.

Figure 9: PDF of galaxy counts in spheres, with best-fit Gumbel overlay for various scales and samples, confirming the prevalence of extreme-value statistics.

Figure 10: Normalized PDFs for $r=20$ and $100$~Mpc/ $h$ ; Gumbel form persists across subsamples, distinct from Gaussian predictions.

Figure 11: Collapse plot of normalized PDF for LRGS in R25, various sphere sizes; Gumbel statistics are robust against finite-size effects.

Implications for Cosmology and Structural Inference

The DESI DR1 conditional density analysis directly contradicts the standard cosmological assumption of statistical homogeneity at $\lambda_0\lesssim 100$ Mpc/ $h$ . The absence of any flattening in $\langle n(r)\rangle$ , slow decay of variance, and non-Gaussian statistics up to $r\sim 400$ Mpc/ $h$ are incompatible with models that generate large-scale structure solely through gravitational instability from initially nearly-uniform density fields. These results imply that galaxy clustering preserves significant correlations on scales previously assumed to be homogeneous, challenging both the limiting arguments for FRW metric applicability and standard galaxy formation theory.

Future Directions

Increasing survey volumes (such as future DESI data releases and Euclid) and improved control over large-scale boundary conditions will allow for more stringent testing of the homogeneity scale and provide opportunities to refine the statistical formalism. It is likely that new theories will be necessary to account for persistent, large-scale correlations, as well as the non-Gaussianity of matter distributions at scales far beyond current model expectations. There are also implications for cosmic variance estimation, baryon acoustic oscillation measurements, and dark energy constraints, which typically assume large-scale homogeneity.

Conclusion

The study reveals no transition to homogeneity in the galaxy distribution up to scales $\sim 400$ Mpc/ $h$ , instead demonstrating persistent power-law clustering, anomalously shallow variance decay, and extreme-value statistics of density fluctuations. These findings present a substantial challenge to current cosmological paradigms and demand reconsideration of the foundational assumptions of large-scale structure formation and inference (2511.21585).