The Back-in-time Void Finder: dynamical identification of cosmic voids through optimal transport reconstruction
Cosmic voids have increasingly emerged as a powerful cosmological probe. However, their large spatial extent and intrinsically underdense environments make their identification highly sensitive to shot noise, redshift-space distortions (RSD), and observational systematics, particularly for topological and density-based void definitions. We introduce the Back-In-Time Void Finder (BitVF), a novel dynamical and physically motivated algorithm that identifies cosmic voids as regions of negative divergence of the Lagrangian displacement field reconstructed from the present-day tracer distribution. The reconstruction relies on an optimized discrete optimal transport algorithm that recovers the backward-in-time dynamics of tracers, naturally accounting for tracer bias without relying on cosmological assumptions. We validate BitVF against the widely used topological void finder REVOLVER using high-resolution N-body simulations, showing that it produces void catalogs with smoother and more physically motivated density profiles, as well as abundances that are more stable under tracer subsampling and shot noise. We further apply it to realistic DESI-like mock light-cone galaxy catalogs, demonstrating that it intrinsically mitigates redshift-space systematic effects, preserving real-space void size functions more faithfully than topological methods. Modeling RSD, the reconstruction can be combined with a fiducial cosmology and an assumed tracer bias within a bias-corrected Kaiser framework, yielding reconstructed-space void catalogs consistent with real-space statistics across redshift. Its performance is characterized as a function of the main internal parameters, showing an optimal balance between accuracy, computational efficiency, and applicability to stage IV galaxy surveys. BitVF will be publicly released within the CosmoBolognaLib.