Large-Scale Galaxy Correlations from the DESI First Data Release

TL;DR

This study uses the conditional galaxy density $\langle n(r)\rangle$ measured from DESI DR1 BGS and LRGS to test the scale of spatial homogeneity, employing fully embedded spheres to mitigate boundary biases and multiple volume-limited subsamples to ensure robust, luminosity-unbiased statistics. It finds a persistent power-law decay $\langle n(r)\rangle \propto r^{-0.8}$ extending up to $r\sim400$ Mpc/$h$, with significant finite-size effects near survey edges and a Gumbel form for the density fluctuation PDF, indicating non-Gaussian, extreme-value statistics. A simplified Cold Dark Matter model predicts a smoother transition to homogeneity around $80$ Mpc/$h$, which is not observed, suggesting tension with standard cosmological expectations of large-scale uniformity. The results underscore the importance of conservative three-dimensional analysis and larger survey volumes to conclusively establish the homogeneity scale, with DESI DR1 laying groundwork for future, more definitive tests of the cosmological principle.

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}/$h$.

Figures (12)

• Figure 1: DESI DR1 angular projection of the DESI DR1 Bright Galaxy Sample (BGS) and Luminous Red Galaxy Sample (LRGS), together with the selected angular regions used in this analysis.
• Figure 2: Upper panels: Redshift distribution of the BGS sample (left panel) and of the LRGS sample (right panel). Bottom panels: Nearest neighbors distribution of the BGS sample (left panel) and of the LRGS sample (right panel).
• Figure 3: Projection in Galactic coordinates on the $x$-$y$ plane of the four volume-limited samples in the region R25: VL2, VL3, VL4, and VL5, from left to right.
• Figure 4: Conditional average density $\langle n(r) \rangle$ (Eq. \ref{['eq:avecon']}) measured in the four volume-limited subsamples --- VL2, VL3, VL4, and VL5 --- extracted from the BGS, as well as from the LRGS. Each panel corresponds to one of the three angular regions: R3, R7, and R25. In the bottom panels it is shown the logarithmic derivative.
• Figure 5: Average conditional density for the LRGS in eight non-overlapping sub-regions of R25. One may note that non-negligible fluctuations, of order $\sim 20\%$, characterize the variation of the average conditional density among these sub-regions.