How deep can a cosmic void be? Voids-informed theoretical bounds in Galileon gravity

TL;DR

The paper identifies a fundamental pathology in Galileon gravity where the non-linear fifth force inside voids can become ill-defined when $1+f_{MG}(z)\,\delta<0$, and develops a background-driven framework using $\mu_{NL}$ and $f_{MG}$ to diagnose viability. It introduces a simple criterion $\max_{0\le z\le z_{in}} f_{MG}(z) \le 1$ and a redshift-dependent void-depth bound $\delta_{min}(z)=\max(-1,-1/f_{MG}(z))$, both computable from background evolution. Applying this to a linear-in-scale-factor parametrization of $(\alpha_B,\alpha_M)$ shows about $60\%$ of the parameter space is excluded, with pathologies typically appearing at $z_{max}\lesssim 10$. The results position cosmic voids as robust, theory-informed priors for viable modified gravity in cosmological inference and can be generalized to other theories with similar non-linear gravitational strength.

Abstract

We establish a general, void-based consistency test for Galileon scalar-tensor theories. We show that the previously reported unphysical breakdown of the predicted Newtonian force in certain Galileon models is controlled by a single condition linking non-linear void dynamics to the cosmic expansion history. This connection yields a redshift-dependent upper bound on the allowed depth of voids and promotes this requirement to a new viability condition, complementary to standard stability criteria. As an example, we apply this void-based criterion to a linear parameterization in the scale factor constrained by theoretical and observational bounds; we find that $\sim 60\%$ of the parameter space is excluded, with most problematic models failing by $z\lesssim 10$. These results position cosmic voids as sharp, broadly applicable, theory-informed filters for viable modified gravity, enabling more informed priors and parameter-space choices in future cosmological inference.

Figures (3)

• Figure 1: $\lvert f_{\rm MG}(z)\,\delta\rvert$ in the $(z,\delta)$ plane for a Galileon model with $(\alpha_{\rm B_0},\alpha_{\rm M_0})=(0.70,0.20)$. White contours mark selected level sets.
• Figure 2: $f_{\rm MG}$ (top panel) and minimum allowed void depth $\delta_{\rm min}(z)$ (bottom panel) as a function of $\ln (1+z)$ for different values of $(\alpha_{\rm B_0},\alpha_{\rm M_0})$.
• Figure 3: Constraints from Eq. \ref{['eq:max_criterion']} in the $(\alpha_{\rm B_0},\alpha_{\rm M_0})$ plane, spanning the ranges allowed at $95\%$ confidence by Noller:2018wyv. Top panel: Maximum value of $f_{\rm MG}(z)$ over $0\leq z\leq 100$, with dashed contours showing isocontours of $\max f_{\rm MG}$. Bottom panel: Viable region (gray) defined by $\max f_{\rm MG}(z)\leq 1$; outside this area, models are excluded and are colour-coded by the redshift $z_{\rm max}$ at which $f_{\rm MG}$ attains its maximum.