Cosmic voids evolution in modified gravity via hydrodynamics

TL;DR

This work develops a hydrodynamical description for the evolution of spherical cosmic voids in modified gravity (MG), encoding deviations from General Relativity through a time- and density-dependent non-linear coupling $ ext{μ}_{ m NL}$ (with the linear limit $ ext{μ}_{ m L}$) that enters the void evolution equation. The framework is applied to luminal Galileon MG models with Vainshtein screening, and a void-informed viability bound is introduced to avoid unphysical imaginary fifth forces, translating into a redshift-dependent minimum void depth. For viable parameter choices, MG induces percent-level enhancements in the non-linear and linear gravitational couplings, yielding percent-level shifts in the void density evolution and modest effects on the Lagrangian-to-Eulerian map and shell-crossing thresholds. The analysis demonstrates that voids reside in an unscreened regime in this MG class, making void observables a sharp probe of late-time MG effects, and provides a consistent bridge from EFT functions to observable void dynamics and constraints.

Abstract

We present a hydrodynamical description of spherical void evolution in modified gravity (MG), extending the standard General Relativity (GR) and dynamical dark energy treatment by encoding gravity modifications into effective couplings that enter the Euler and Poisson equations. This yields a compact non-linear evolution equation for the Eulerian density contrast, controlled by a time- and density-dependent effective gravitational strength, and provides a direct map between model functions and void observables. We apply the framework to the luminal Galileon class of models, where derivative self-interactions generate Vainshtein screening and might lead to a breakdown of the physical branch in sufficiently underdense regions. Exploiting this feature, we apply the void-informed viability requirement that translates into bounds on the theory parameter space and, equivalently, on the minimum attainable void depth as a function of redshift. For viable parameters of a concrete model, we quantify the impact of MG on isolated void evolution, the Lagrangian to Eulerian mapping, and the shell-crossing threshold. Relative to GR, we find a clear hierarchy of MG effects, with ${\cal O}(10\%)$ modifications in the gravitational couplings, percent-level shifts in the void density evolution, and sub-percent deviations in both the mapping and the shell-crossing thresholds. Moreover, within the adopted parametrization, we show analytically that voids always lie in an unscreened regime on the physical branch. Overall, the formalism provides a self-consistent route to predict void dynamics and consistency constraints in a broad class of MG models.

Figures (13)

• Figure 1: Void-informed viability across the $(\alpha_{\rm B_0},m)$ plane for the baseline background parameters given in eq. \ref{['eq:baseline_background']}. The scanned ranges correspond to the $1\sigma$ combined constraints of Traykova:2021hbr for the $\Lambda=0$ branch. Left: maximum value attained by $f_{\rm MG}(z)$ over $0\le z\le 100$ for each parameter point, with contours indicating constant values of this maximum. Right: models satisfying the void-informed bound in eq. \ref{['Eq:viability_criterion_voids_MG']}, shown as the gray region. Outside the gray region, models are excluded and are color coded by the redshift $z_{\rm max}$ at which $f_{\rm MG}(z)$ reaches its maximum.
• Figure 2: Evolution of $f_{\rm MG}(z)$ and $\delta_{\min}(z)$ as a function of redshift (top and bottom rows, respectively). The left column varies $\alpha_{\rm B_0}\in\{0.3,0.5,0.7,0.9\}$ at fixed $m$, while the right column varies $m\in\{2.1,2.3,2.5,2.7\}$ at fixed $\alpha_{\rm B_0}$. In each panel, the remaining parameters are set to the best fit of Traykova:2021hbr, $\alpha_{\rm B_0}=0.6$ and $m=2.4$.
• Figure 3: The evolution of $\delta_{\rm min}(z)$, $\delta_{\rm min,p}(z)$, $\delta_{\rm min,h}(z)$, and $\delta_{\rm min,p_0}(z)$ over $z\in[0,4]$ for two representative MG models. Left:$(\alpha_{\rm B_0},m)=(0.6,2.4)$. Right:$(\alpha_{\rm B_0},m)=(0.8,2.7)$.
• Figure 4: Non-linear $\mu_{\rm NL}$ (top row) and linear gravitational coupling $\mu_{\rm L}$ (bottom row) shown over $z\in[0,1]$. Left column: varying $\alpha_{\rm B_0}\in\{0.3,0.5,0.7\}$ at fixed $m=2.1$. Right column: varying $m\in\{2,2.05,2.10\}$ at fixed $\alpha_{\rm B_0}=0.7$. In all cases, the background parameters, including those of the reference $w_0w_a$CDM model, are fixed to the baseline cosmology specified in eq. \ref{['eq:baseline_background']}.
• Figure 5: Auxiliary function $g(\tilde{y})$ defined in eq. \ref{['eq:g_y']}, shown over $\tilde{y}\in[-4,4]$. The intervals $\tilde{y}>0$ and $\tilde{y}\in[-1,0)$ correspond to halos and voids, respectively, while $\tilde{y}<-1$ marks the pathological regime where $g(\tilde{y})$ becomes imaginary. The point $\tilde{y}=0$ corresponds to the unperturbed background and serves as a limiting value, with no direct physical meaning as a separate configuration.