A spherical hydrodynamical model of cosmic voids in ΛCDM and beyond

TL;DR

The paper develops a novel hydrodynamical framework to model spherical cosmic void evolution, deriving a cosmology-dependent mapping between the linear (Lagrangian) and non-linear (Eulerian) density contrasts and a generalized shell-crossing criterion valid beyond Einstein–de Sitter. Applying this to ΛCDM and dynamical dark energy models (w0CDM and w0w_aCDM), it shows voids are notably sensitive to Ω_m,0 and w0 (up to 20–30% changes in the non-linear density contrast), with w_a having a smaller, but detectable, impact. A cosmology-dependent δ_v(z, δ_E) mapping is constructed to connect initial underdensities to late-time Eulerian void observables, enabling precise void statistics such as the void size function to probe the expansion history. The results highlight the potential of precision void analyses to constrain dynamical dark energy and motivate public release of the associated numerical code for broader use in cosmology.

Abstract

Cosmic voids have emerged as powerful probes for cosmology, providing complementary information on the large-scale structure of the universe. We present the first application of a hydrodynamical framework to model the evolution of cosmic voids. This approach offers a physically intuitive characterization of void dynamics and can naturally be applied to non-standard cosmologies. We derive the cosmology-dependent mapping that relates the linear (Lagrangian) and fully non-linear (Eulerian) evolution of the matter density contrast, a central component for accurate theoretical modeling of void statistics. Furthermore, we present a new method for determining the shell-crossing epoch across arbitrary cosmological backgrounds, thereby extending previous treatments restricted to the Einstein-de Sitter universe. Motivated by recent DESI results hinting at dynamical dark energy, we investigate void evolution in $ w_0w_a$CDM cosmologies by varying $ w_0$ and $w_a$. We also consider the impact of varying the matter density parameter, $ Ω_{\mathrm{m},0}$. We find that the evolution of isolated, spherically symmetric cosmic voids is most sensitive to $ Ω_{\mathrm{m},0} $ and $ w_0 $, which can alter the non-linear density contrast by up to 20-30%. Variations in $w_a$ have a smaller impact, but may still lead to measurable effects. We also show that the cosmology-dependent mapping between linear and non-linear density contrasts may provide a sensitive probe of dynamical dark energy in precision void analyses.

Figures (17)

• Figure 1: The continuous density profile $\delta_{\rm E}$ is shown as a function of the initial physical radial coordinate $r_{\rm in}$ for a spherical void with initial radius $r_{\rm v,in}$. The void is embedded in a cosmological background environment, defined as the region where matter perturbations are absent. Here, $r_\ast$ marks the radius at which the matter density contrast $\delta_{\rm E}$ ceases to be constant and starts to increase.
• Figure 2: Evolution of $\delta_{\rm E}$ (top panels) and $\delta_{\rm L}$ (lower panels) as functions of redshift in the range $z \in [0, 2.5]$ for different cosmological models. In the left column, we fix $(w_0 = -1, w_a = 0)$ and vary the present-day matter density parameter $\Omega_{\mathrm{m},0}$. In the central columns, we fix $(\Omega_{\rm m,0} = 0.32, w_a = 0)$ while varying $w_0$. In the right column, we fix $(\Omega_{\rm m,0} = 0.32, w_0 = -1)$ while varying $w_a$. The initial conditions ($\delta_{\rm v,in}$ at $x_{\rm in}$) for all the solutions shown are identical and correspond to those that, in an EdS model, lead to $\delta_{\rm E}(z=0) = -0.5$.
• Figure 3: The redshift of matter–dark energy equality, $z_{\rm eq}$, defined by $\rho_{\rm m}(z_{\rm eq}) = \rho_{\rm DE}(z_{\rm eq})$, as a function of $w_0$ and $w_a$, while keeping $\Omega_{\rm m,0} = 0.32$ fixed.
• Figure 4: Percentage relative difference in the non-linear matter density contrast $\delta_{\rm E}$ between $w_0w_a$CDM and $\Lambda$CDM models, plotted as a function of redshift. In all panels, the matter density is fixed to $\Omega_{\mathrm{m},0} = 0.32$, while $w_a$ is varied over the range $[-2, 0.1]$. Each column corresponds to a different choice of $w_0$, with values $-1$, $-0.8$, $-0.6$, and $-0.4$ from left to right.
• Figure 5: Relative percentage difference between the non-linear density contrast $\delta_{\rm E}(z)$ in $\Lambda$CDM and in an EdS universe, shown as a function of redshift in the interval $z \in [0,1]$. In this setup, we fix the "late-time" condition (see section \ref{['Sec:hydrodynamical_approach']}) at $z = 99$ by sampling $\delta_{\rm E}(z=99)$ within the range $[-0.05\,,-0.001]$, as specified in eq. \ref{['Eq:range_ICs']}, and then evolve each case down to redshift zero. All differences are computed with respect to the EdS solution, using the same conditions at $z = 99$.