A spherical hydrodynamical model of cosmic voids in ΛCDM and beyond

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.

💡 Research Summary

This paper introduces a novel hydrodynamical framework for modeling the evolution of isolated, spherically symmetric cosmic voids, extending the classic spherical collapse model to a pressure‑less fluid description that is directly derived from the continuity, Euler, and Poisson equations in an expanding Friedmann‑Lemaître‑Robertson‑Walker (FLRW) background. The authors’ primary goal is to construct a cosmology‑dependent mapping between the linear (Lagrangian) density contrast, δ_L, and the fully non‑linear (Eulerian) density contrast, Δ_E, which is essential for accurate theoretical predictions of void statistics such as the Void Size Function (VSF).

Key methodological advances

1. Hydrodynamical formulation – By treating matter as a pressureless fluid, the evolution equations reduce to a set of ordinary differential equations for the void radius R(t) and the average density contrast Δ(t). The approach naturally separates the growing mode from the decaying mode, allowing clean initial conditions based on a top‑hat density profile.

2. Generalized shell‑crossing criterion – In the Einstein‑de Sitter (EdS) universe, shell‑crossing (the moment when fluid shells intersect, breaking the bijective Lagrangian‑to‑Eulerian map) occurs at a well‑known linear extrapolation δ_sc ≈ –2.71. The authors derive a numerical procedure to locate the shell‑crossing epoch for arbitrary background cosmologies, including ΛCDM and time‑varying dark‑energy models w₀wₐCDM. The algorithm identifies the time when dR/dt → 0 and the density contrast steepens sharply, ensuring a consistent definition of the void formation threshold across models.

3. Cosmology‑dependent linear‑to‑non‑linear mapping – Using the hydrodynamical evolution together with the generalized shell‑crossing condition, the paper constructs a mapping function M(δ_L; Ω_m0, w₀, wₐ) that translates any given linear contrast into its non‑linear counterpart at the epoch of interest. This mapping is shown to be highly sensitive to the matter density parameter Ω_m0 and the present‑day dark‑energy equation‑of‑state parameter w₀, while the evolution of wₐ (the time‑variation of w) produces a comparatively modest effect.

Results of the parameter study

• Varying Ω_m0 within a realistic range (0.25–0.35) changes the final non‑linear density contrast of a void by up to 20–30 %. Higher Ω_m0 deepens voids because the stronger matter content slows the expansion of underdensities.
• Changing w₀ from –1 (cosmological constant) to –0.8 (less negative pressure) yields a similar magnitude of change in Δ_E, reflecting the reduced acceleration of the background expansion.
• Adjusting wₐ in the interval