The Back-in-time Void Finder: dynamical identification of cosmic voids through optimal transport reconstruction

TL;DR

Cosmic voids offer cosmological leverage but are challenging to identify reliably due to shot noise and redshift-space distortions. The Back-in-time Void Finder (BitVF) uses an optimal-transport reconstruction to recover the backward-in-time Lagrangian displacement field and defines voids as regions of negative divergence $\nabla_\mathbf{q}\cdot\boldsymbol{\Psi}<0$, with voids delineated by a watershed on the divergence field. The approach is validated against a topological void finder on high-resolution N-body data and tested on DESI-like light-cone mocks, showing smoother void density profiles, more stable abundances under subsampling, and intrinsic mitigation of RSD effects; when combined with a bias-corrected Kaiser mapping, BitVF reconstructs real-space void statistics across redshift with high fidelity. The BitVF framework, implemented within CosmoBolognaLib, offers a robust, scalable dynamical void finder suitable for stage IV surveys and enables accurate cosmological inferences from void statistics using reconstructed dynamics.

Abstract

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.

Figures (20)

• Figure 1: Two possible configurations of a quartet of displacement vectors are shown. The configuration that minimizes the total distance between $\mathbf{x}$ and $\mathbf{q}$ positions is saved, while the other possible solutions are discarded.
• Figure 2: Left: Example of a light-cone cell, defined by the intersection of two concentric spheres, two meridional planes, and two cones whose vertices lie at the center of the Cartesian coordinate system and whose axes coincide with the polar axis. Right: The same cell located at a large comoving distance from the observer, where its geometry becomes approximately cubic.
• Figure 3: A $5 \,h^{-1}\mathrm{Mpc}$-thick slice extracted from the $500^3 \,h^{-3}\mathrm{Mpc}^3$ core of the Aletheia halo sample. The figure shows the resulting watershed segmentation of the divergence field, with voids shown in light blue and their boundaries in orange. Regions of positive divergence (overdensities) are shown in white, while halos are shown in black.
• Figure 4: Top: VSFs for the 1%, 10%, and full halo samples, shown in purple, green, and orange, respectively. The errorbars represent the associated Poissonian error, while the shaded bands indicate the standard deviation for the void counts across the 100 runs, for each sample. Bottom: The ratios between the intrinsic stochastic error of the method and the Poissonian error.
• Figure 5: A slice of $20 \,h^{-1}\mathrm{Mpc}$ thickness from the $500^3 \,h^{-3}\mathrm{Mpc}^3$ core of the halo sample from the Aletheia simulations. Different stages of the void identification procedure are shown. (a) The Eulerian positions of the halos at $z\!=\!0$. (b) The reconstructed velocities of the halos. (c) The divergence field superimposed on the halo positions. Blue regions indicate zones with negative divergence of the back-in-time displacement field, corresponding to regions from which halos tend to escape when evolved forward in time. Red regions indicate positive divergence, marking regions of local mass inflow. (d) The same as panel c, with the identified voids overplotted. Voids are identified using the watershed algorithm introduced above and are represented as circles for graphical clarity.