Everything Everywhere All At Once: A Hierarchical Framework for Mapping Anisotropies in the Local Universe

Abstract

We present a Bayesian hierarchical forward model for mapping the local luminosity-density field from heterogeneous redshift surveys. By dividing the survey volume into angular cells and redshift shells, we model the observed galaxy distribution directly in apparent-magnitude and redshift space. This allows us to infer cell-level luminosity functions and densities while preserving each survey's unique selection function. Simultaneously, the ensemble of cells constrains the cosmic-mean luminosity function, its redshift evolution, and the hyperparameters describing cell-to-cell variation. We apply the framework to 2MRS, 6dFGS, and GAMA over $0.005<z<0.065$, combining wide sky coverage with deeper and fainter galaxy samples. The model successfully recovers global $J$-band luminosity-function parameters and a mean luminosity density consistent with previous low-redshift measurements. The inferred luminosity-density scatter decreases with volume, consistent with the cosmic-variance amplitude expected in a $Λ$CDM universe. Within the volume we probe, we find no evidence for a large coherent underdensity. Instead, the local Universe is broadly consistent with smooth evolution and cosmic variance. The nearest shell at $z \simeq 0.01$ is the clearest exception, lying $\simeq 0.12$~dex ($\simeq 25\%$) below the smooth global model, a $-2.6σ$ underdensity with a one-sided significance of $\simeq 99.5\%$. This framework offers a scalable architecture for mapping cosmic density fields with next-generation wide and deep surveys.