Bayesian Cosmic Void Finding with Graph Flows

TL;DR

This paper introduces a probabilistic method using graph neural networks to identify cosmic voids from galaxy surveys, capturing the inherent uncertainties and improving cosmological information extraction.

Contribution

It presents a novel stochastic approach to void finding that generalizes traditional algorithms and enables Bayes-optimal mapping between galaxies and voids.

Findings

The method performs well in simplified tests, showing good stochasticity and regularization.

Cosmological information from the predicted voids exceeds that of the deterministic teacher.

The approach can emulate existing void finders and potentially generalize to complex definitions.

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.