Bayesian Cosmic Void Finding with Graph Flows

TL;DR

A method to sample from the stochastic mapping from galaxy catalogs to arbitrary void definitions, which uses a deep graph neural network to evolve "test particles" according to a flow-matching objective and allows us to find the Bayes-optimal mapping between observed galaxies and any void definition.

Abstract

Cosmic voids contain higher-order cosmological information and are of interest for astroparticle physics. Finding genuine matter underdensities in sparse galaxy surveys is, however, an underconstrained problem. Traditional void finding algorithms produce deterministic void catalogs, neglecting the probabilistic nature of the problem. We present a method to sample from the stochastic mapping from galaxy catalogs to arbitrary void definitions. Our algorithm uses a deep graph neural network to evolve "test particles" according to a flow-matching objective. We demonstrate the method in a simplified example setting but outline steps to generalize it towards practically usable void finders. Trained on a deterministic teacher, the model performs well but has considerable stochasticity which we interpret as regularization. Cosmological information in the predicted void catalogs outperforms the teacher. On the one hand, our method can cheaply emulate existing void finders with apparently useful regularization. More importantly, it also allows us to find the Bayes-optimal mapping between observed galaxies and any void definition. This includes definitions operating at the level of simulated matter density and velocity fields.

Figures (11)

• Figure 1: Illustration of the instability of deterministic void finders. Four times, the same galaxies are randomly jittered by $\sigma=1\,h^{-1}\text{Mpc}$. The corresponding VIDE voids are shown as circles (matching in effective radius). There are substantial differences between the void catalogs.
• Figure 2: Validation loss curves for final production runs (orange, green) and illustrative trial runs with smaller models (blue, purple). At the indicated points, the random jittering of target void positions was decreased to the final value.
• Figure 3: Slab of $100\,h^{-1}\text{Mpc}$ thickness in a test sample. Grey points are galaxies and black crosses ground-truth VIDE voids. Test particles are randomly initialized in the filled orange circles and then evolved by the graph network along the orange trajectories. The test particles also carry a prediction of void volume which is not visualized. See Fig. \ref{['fig:trajsamples']} in the appendix for multiple random initializations of the test particles.
• Figure 4: Check for the consistency condition that, in expectation, number of converging test particles should be proportional to void volume.
• Figure 5: Summary statistics of galaxy voids at the fiducial cosmology and HOD. Black is VIDE ground truth, orange our model's prediction. Top panel: void size function. Bottom panel: void-galaxy and void-void correlation functions.