Persistence of the conditional-density power-law beyond 200 Mpc/h

Determine whether the conditional average galaxy density measured in the DESI DR1 Bright Galaxy Sample and Luminous Red Galaxy Sample continues to follow a power-law scaling with exponent γ ≈ 0.8 at scales r ≳ 200 Mpc/h, or whether there is a slow transition to spatial homogeneity or a weaker, possibly logarithmic, scale dependence.

Background

The paper measures the conditional average density of galaxies—defined as the mean density within spheres of radius r centered on galaxies—using DESI DR1 Bright Galaxy (BGS) and Luminous Red Galaxy (LRGS) samples. Across multiple volume-limited subsamples and angular regions, the conditional density exhibits a scale-invariant decay approximately as r^{-0.8} up to hundreds of megaparsecs, with no clear transition to homogeneity within the surveyed volumes.

Finite-size and boundary effects become increasingly significant near the largest probed scales, and the distribution of density fluctuations follows a Gumbel distribution rather than a Gaussian, suggesting persistent large-scale inhomogeneities. The authors explicitly note uncertainty about whether the observed r^{-0.8} behavior persists beyond r ≳ 200 Mpc/h, or whether a gradual transition to homogeneity or weaker, possibly logarithmic, scaling occurs.