The era of precision cosmology with voids

TL;DR

This review addresses how cosmic voids can drive precision cosmology by exploiting their simple dynamics, large volumes, and sensitivity to fundamental physics. It surveys a broad suite of void observables (VSF, VGCF, velocity profiles, lensing, CMB cross-correlations) and the theoretical frameworks (excursion-set, peak theory, bias expansions) that connect void statistics to cosmological parameters. It also discusses observational systematics, reconstruction approaches, and the current constraints from surveys like BOSS, eBOSS, and DES, plus forecasts for Euclid, Roman, CSST, SPHEREx, DESI-II, and WST. The review highlights the orthogonal constraining power of voids relative to standard probes, and emphasizes their role in testing dark energy, modified gravity, and neutrino masses, with substantial gains anticipated from upcoming large-volume surveys. In short, cosmic voids are poised to complement and extend ΛCDM constraints, turning emptiness into a frontier for fundamental physics, formalized through the equation of state $w(a)=w_0+(1-a)w_a$ and related growth and geometry parameters.

Abstract

Cosmic voids, the large underdense regions of our Universe, have emerged over the past decade as powerful cosmological laboratories: their simple dynamics, sensitivity to local gravitational effects and cosmic expansion, and ability to span large volumes, make them uniquely suited to test fundamental physics. Fueled by advances in theory, simulations, and observations, void science has matured into a precision tool for constraining the parameters of the standard cosmological model and its possible extensions. In this review, we provide a comprehensive description of the statistical tools developed to characterize voids, the theoretical models that link them to cosmological parameters, and the methodologies used to extract information from survey data. We highlight the growing synergy between void-based observables and other cosmological probes, and showcase the increasingly stringent constraints derived from voids measured from current survey data and expected from future missions. With the advent of the next generation of galaxy surveys, voids are poised to play a central role in the future of cosmology, turning what was once regarded as emptiness into one of the most promising frontiers of fundamental science.

Figures (18)

• Figure 1: Visual representation of cosmic voids found with VIDE (left) and Sparkling (right). We show with different colors the voids identified by the two algorithms in the distribution of dark matter halos (black dots) extracted from the AbacusSummit simulation suite at $z=0.2$. Both panels cover the central part of the box and represent the 2D projection of a $30 \ h^{-1} \, \mathrm{Mpc}$ slice along the Z-axis.
• Figure 2: Comparison between the VSFs measured using cosmic voids identified with VIDE (left) and Sparkling (right) in the AbacusSummit simulation suite, using dark matter particles as tracers. In both panels, different colors indicate the VSF at different redshifts: $z = 0.2$ in blue, $z = 0.5$ in purple, and $z = 1.1$ in red. Shaded regions represent the uncertainty in each bin, derived from the Poisson error as $\sqrt{N}/(V \, \Delta\ln R_{\rm v})$, where $N$ is the counts of voids in the finite logarithmic bin $\Delta \ln R_{\rm v}$ and $V$ the volume occupied by the cosmic tracers.
• Figure 3: Comparison between the differential density contrast profiles measured using cosmic voids identified with VIDE (left) and Sparkling (right) in the AbacusSummit simulation suite, using dark halos at $z=0.2$ as tracers. In both panels, the void sample is split in equi-populated bins, starting from 2.5 times the mean separation of the halo catalog and extending up to the largest void radius of each sample. Within each bin, voids with similar effective radii are averaged together, and the resulting density contrast profile is represented with different colors according to the void size.
• Figure 4: Same as \ref{['fig:delta_comparison']}, but for void radial velocity profiles.
• Figure 5: Comparison between the auto-correlation function extracted from voids identified with VIDE (left) and Sparkling (right), using the same simulations introduced for \ref{['fig:VSF_comparison']} but selecting voids with radius greater 2.5 times the mean separation of the dark matter particles. Here both measures are multiplied by the squared distances between the pairs of void centers in order to enhance the signal.