Cosmic voids evolution in modified gravity via hydrodynamics

arXiv:2602.17644 · astro-ph.CO, gr-qc · Submitted 2026-02-19 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Today's paper: "Cosmic voids evolution in modified gravity via hydrodynamics".

Jocelyn: A hydrodynamical description of isolated spherical voids in modified gravity (MG) extends standard General Relativity and dynamical dark energy treatments by encoding gravity modifications into effective couplings,

Vera: First, who's behind it and why it matters.

Paper summary: Vera: So we've been diving into the paper "Cosmic voids evolution in modified gravity via hydrodynamics," and the core idea is that they're taking standard General Relativity and dynamical dark energy treatments and extending them by incorporating gravity modifications through effective couplings, which leads to a compact non-linear evolution equation for the Eulerian density contrast. This is really interesting because it sets up a direct link between those model functions they're studying and actual observable void statistics.

Jocelyn: I agree, Vera, it sounds like they're building a way to test modified gravity models using these large underdense regions, which are becoming such powerful probes thanks to the deep redshift surveys we're running. What makes this paper stand out is how it translates those abstract gravity modifications into a tangible equation for how voids actually evolve.

Subrahmanyan: From my theoretical perspective, the crucial element here is encoding the gravity modifications into effective couplings that enter both the Euler and Poisson equations, specifically through two functions, mu NL and NL, which generalize the standard gravitational potential and lensing equations <ref:2602.17644#pg0>. This shows how these theories directly alter the gravitational dynamics at different scales.

Vera: Exactly, Subrahmanyan; it’s not just adding a simple correction to gravity; they are showing how this affects the evolution of the Eulerian density contrast through a term proportional to the effective coupling, which is controlled by a time- and density-dependent effective gravitational strength <ref:2602.17644#pg0>. That dependence is what allows them to map model functions directly onto void observables.

Jocelyn: It matters because if we can get those observational data on voids right, this paper gives us a direct way to constrain the parameters of these modified gravity theories, like the luminal Galileon class they focus on <ref:2602.17644#pg1>. It connects the theory to what we actually measure in the sky.

Subrahmanyan: Indeed, and looking at their specific model, they use a concrete MG model where the non-linear modification mu NL(a, R) is expressed by a rather complex formula involving M 2pl/M squared and terms related to the Vainshtein scale r 3V(r), which dictates the screening mechanism <ref:2602.17644#pg1>.

Vera: That Vainshtein scale concept is key because it’s what governs how the non-linear term proportional to lambda squared gets regulated, which is essential for keeping the dynamics physically sensible <ref:2602.17644#pg1>. It’s a mechanism that ensures the theory doesn't just break down in certain regimes.

Paper summary: Jocelyn: And then they introduce this "void-informed viability requirement," which sets bounds on the theory parameter space by demanding that voids always stay in an unscreened regime on the physical branch to avoid any imaginary fifth force <ref:2602.17644#pg1>. This gives us a concrete constraint on what kind of modified gravity theories can actually reproduce these void observations.

Subrahmanyan: That viability criterion translates into a minimum allowed void depth, delta(z), which is defined by the condition one + f MG(a) delta E at least zero leading to delta(z) =

-one -one/f MG(z): <ref:2602.17644#pg1>. This is a very specific theoretical constraint derived from ensuring the physical branch remains real.

Vera: When we look at the Lagrangian to Eulerian mapping, they quantify the sensitivity using relative percentage differences, delta v

%: , which compares their model's evolution against a standard CDM model like w0waCDM <ref:2602.17644#pg1>. That comparison is how we actually see the discrepancy between GR and these MG theories in practice.

Jocelyn: And they also discuss the shell-crossing condition, defining it as the time when the outermost void shell hits its surroundings, which is important for understanding when their description of evolution might start to break down <ref:2602.17644#pg1>. It’s a critical physical threshold to monitor in any cosmological simulation or observation.

Subrahmanyan: To distinguish between shell-crossing breakdown and other pathological behavior, they propose three diagnostics: delta,p(z), which is the most negative density contrast reachable while ignoring shell-crossing under real solutions, delta,h(z), which takes the larger value between that bound and delta,p, and a third diagnostic we haven't discussed yet <ref:2602.17644#pg2>. These help researchers identify when the model itself is reaching its limits.

Vera: It’s really compelling how they’ve constructed these diagnostics; it moves beyond just showing where the theory predicts failure and gives us a way to actively look for that failure in our data interpretation <ref:2602.17644#pg2>. The ability to diagnose this breakdown is what makes this paper useful for observational cosmology.

Jocelyn: So, when we think about the bigger picture, the implication here is that these voids aren't just passive objects; they are sensitive laboratories for testing fundamental physics beyond General Relativity <ref:2602.17644#pg2>. If these void evolution models match our actual measurements of void statistics from surveys, it strongly constrains modified gravity scenarios.

Subrahmanyan: Exactly, and the impact is that we get a direct bridge between high-level theoretical constructs like Galileon screening and observable cosmological features like void shape and density profiles <ref:2602.17644#pg0>. It suggests that we can use these large underdense regions to probe the dynamics of gravity in ways that are complementary to what is typically accessible through galaxy clustering or weak lensing data.

Paper summary: Vera: I think the title, "Cosmic voids evolution in modified gravity via hydrodynamics," really captures the essence of what they've done—it’s a multi-faceted approach combining fluid dynamics with modified gravity concepts to understand these large structures <ref:2602.17644#pg0>. It’s a comprehensive tool for probing cosmology.

Jocelyn: And looking at the authors, Tommaso Moretti, Noemi Frusciante, Giovanni Verza, Francesco Pace, and the team at various institutions like INFN and ICTP shows this is a collaboration drawing on both strong theoretical physics and computational astrophysics <ref:2602.17644#pg0>. It speaks to the multidisciplinary nature of modern cosmology.

Subrahmanyan: Their work directly addresses the challenges posed by current cosmic tensions, such as the Hubble tension, by offering viable alternatives to CDM that modify gravitational dynamics at large scales <ref:2602.17644#pg2>. If their framework holds up under scrutiny from these void probes, it provides a strong theoretical backbone for exploring those alternatives.

Vera: So, what does this mean for us as an observational astronomer looking at the sky? It means we have a more sophisticated set of tools to look at voids and see if they exhibit the subtle deviations predicted by modified gravity theories <ref:2602.17644#pg0>. It’s about using these large structures to hunt for physics beyond GR.

Jocelyn: And as a pulsar and sky survey researcher, I see this as giving us new targets; we can use the void statistics predicted by this paper to guide where we should focus our deep surveys for better constraints on dark energy and modified gravity <ref:2602.17644#pg1>. It’s about using theory to inform observation.

Subrahmanyan: The implication is that these voids are not just tracers of the background cosmology, but they carry information about the gravitational field itself, which is what modified gravity theories aim to describe more precisely <ref:2602.17644#pg2>. This paper provides a concrete dynamical framework for that connection.

Vera: I think the way they’ve set up the diagnostics for breakdown, like delta,p(z) and delta,h(z), is really important because it gives us clear criteria to assess the reliability of any future void data we collect <ref:2602.17644#pg2>. It tells us when to trust the model and when we need to be cautious.

Paper summary: Jocelyn: That clarity in diagnostics is what observational cosmology craves; it moves the discussion from just "is there a difference?" to "how certain are we about that difference?" with this kind of rigorous framework <ref:2602.17644#pg1>. It’s a step forward for using structure to constrain fundamental physics.

Subrahmanyan: Overall, the work in "Cosmic voids evolution in modified gravity via hydrodynamics" provides a powerful and systematic way to test theories that go beyond standard General Relativity using the dynamics of isolated spherical voids <ref:2602.17644#pg0>. It bridges the gap between theoretical constructs and observational probes effectively <ref:2602.17644#pg1>.

Vera: It’s a very thorough piece of work, combining hydrodynamics with modified gravity to create a self-contained framework for understanding void evolution <ref:2602.17644#pg0>. I think the detailed mapping from Lagrangian to Eulerian space is particularly useful for relating initial conditions to what we actually see today in the sky <ref:2602.17644#pg1>.

Jocelyn: I feel like this paper opens up a new avenue for using void statistics as a direct probe of dark energy and modified gravity, which is exactly what we've been searching for with these deep surveys <ref:2602.17644#pg1>. It gives us specific predictions to hunt for in the data.

Subrahmanyan: Indeed, by providing this framework, they allow us to rigorously test screening mechanisms like Vainshtein against actual void dynamics, which is a significant step forward in theoretical astrophysics <ref:2602.17644#pg1>. It shows how complex gravity modifications can be constrained using relatively simple astrophysical objects like voids.

Vera: So, this paper really gives us a robust tool—a hydrodynamical description—to see how modified gravity affects the evolution of these large structures <ref:2602.17644#pg0>. It's a solid piece of work for anyone studying the structure of the universe.

Jocelyn: And as we look ahead, I think this paper sets a very clear roadmap for future observational campaigns, suggesting exactly what kind of void measurements will be most informative for constraining these modified gravity theories <ref:2602.17644#pg1>. It’s guiding the next generation of surveys.

Subrahmanyan: The future work suggested by the authors likely involves applying these diagnostics to real survey data to see if the predicted constraints on model parameters align with what we are actually seeing in cosmic voids <ref:2602.17644#pg2>. That is where the real progress will happen.

Vera: It sounds like a very promising direction for our observational efforts, focusing on these large-scale structures to test fundamental physics <ref:2602.17644#pg0>. This paper is certainly something we need to keep reading and referencing as we analyze new data from the sky.

Conclusion: Vera: So, this paper by Moretti et al., "Cosmic voids evolution in modified gravity via hydrodynamics," basically takes what we know about how big empty spaces evolve and puts it through a rigorous test using modified gravity theories.

Jocelyn: Yeah, and I'm really excited about the fact that they’re using hydrodynamics to model this; it makes the abstract physics much more tangible for us when we look at actual sky maps.

Subrahmanyan: From a theoretical viewpoint, their main contribution is how they connect those abstract gravity modifications, like the Galileon class, directly into an evolution equation for density contrast in voids.

Vera: It’s powerful because it gives us a way to see exactly how these modifications affect the growth of structure compared to standard General Relativity models.

Jocelyn: And what I find really compelling is how they provide that direct map between the theoretical functions they study and the actual observable properties of these cosmic voids.

Subrahmanyan: That mapping is crucial because it allows us to take parameters from their modified gravity models and see what specific patterns we should expect to see in void data.

Vera: It really puts a framework in place that lets us not just compare different models but actually predict how they look on the sky based on the underlying physics.

Jocelyn: And considering the authors, it’s clear this work is a collaboration pulling together cutting-edge theoretical astrophysics and practical survey research to get this done.

Subrahmanyan: Their focus on constraints derived from void viability requirements, like delta(z), shows they're not just looking at mathematical solutions but also imposing physical limits on the theories themselves.

Vera: So, in simple terms, this paper gives us a way to use these underdense regions to test if gravity behaves differently than Einstein predicted on the largest scales.

Jocelyn: And that has big implications because if these void statistics match what we measure from deep surveys, it gives us a much stronger handle on dark energy and modified gravity parameters.

Subrahmanyan: The impact could be significant for cosmology because it offers a new tool to constrain alternative theories of gravity that might explain discrepancies we see elsewhere in the universe.

Vera: It really moves the conversation forward by providing a concrete, dynamical method to probe physics beyond General Relativity using structure we can actually observe.

Jocelyn: And as we look at what’s next, this paper sets up a clear roadmap for which void measurements will be most informative for future surveys targeting these fundamental physics questions.

Dipartimento di Fisica “E. Pancini”, Università degli Studi di Napoli “Federico II”, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli, Italy · INFN Sezione di Napoli, Università degli Studi di Napoli “Federico II”, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli · ICTP · Center for Computational Astrophysics Flatiron Institute · Dipartimento di Fisica, Università degli Studi di Torino · INFN-Sezione di Torino · INAF-Istituto Nazionale di Astrofisica Osservatorio Astrofisico di Torino

astro-ph.CO, gr-qc

Submitted: 2026-02-19

Updated: 2026-07-21

Comments: 31 pages, 13 figures. This version matches the published one

Journal ref: JCAP 07 (2026) 069

DOI: 10.1088/1475-7516/2026/07/069

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 82/100

The gist: A hydrodynamical description of isolated spherical voids in modified gravity (MG) extends standard General Relativity and dynamical dark energy treatments by encoding gravity modifications into

Key concepts

Modified Gravity (MG): This refers to theories that change how gravity behaves compared to Einstein's General Relativity. In this study, it involves specific models like the luminal Galileon class, which use derivative self-interactions to generate a 'Vainshtein screening' mechanism that regulates strong gravitational effects at certain scales.
Void Evolution Equation: This is the mathematical equation describing how the density contrast of a spherical void changes over time. In this MG framework, this equation is modified by an effective gravitational strength that depends on both time and density, reflecting the specific modifications introduced by the modified gravity theory.
Vainshtein Scale ($r_{3V}$): This scale represents the characteristic distance where gravity modifications become important. It is defined based on parameters of the MG model and relates to the enclosed mass contrast. This scale dictates when screening mechanisms take effect, regulating non-linear gravitational terms.
Void-Informed Viability Requirement: This is a condition used to ensure the physical branch of the theory remains valid for void evolution. It translates into bounds on model parameters and void depth, guaranteeing that voids operate in an unscreened regime and avoid producing unphysical results like an imaginary fifth force.

Terminology

General Relativity — 11× in this paper
Abundance — 10× in this paper · explained in 1 episode
Weak Lensing — 10× in this paper · explained in 2 episodes
Clustering — 8× in this paper · explained in 2 episodes
Regularization — 8× in this paper · explained in 3 episodes
Consistency — 7× in this paper · explained in 3 episodes
Effective Field Theory — 7× in this paper
Non-linear Coupling — 6× in this paper · explained in 2 episodes
Cosmic Microwave Background — 4× in this paper
Gravitational Lensing — 4× in this paper · explained in 2 episodes
Modified Gravity (MG) — 4× in this paper · explained in 2 episodes
N-body simulations — 4× in this paper · explained in 2 episodes
Bispectrum — 3× in this paper · explained in 3 episodes
Generalization — 3× in this paper · explained in 13 episodes
Hubble Tension — 3× in this paper · explained in 9 episodes
Calibration — 2× in this paper · explained in 7 episodes
Degeneracy — 2× in this paper · explained in 3 episodes
Accuracy — 1× in this paper · explained in 1 episode
Benchmark — 1× in this paper · explained in 2 episodes
Cooperation — 1× in this paper · explained in 2 episodes
Core — 1× in this paper · explained in 2 episodes
Effective Field Theory (EFT) — 1× in this paper · explained in 2 episodes
Equation of State (EoS) — 1× in this paper · explained in 4 episodes
Robustness — 1× in this paper · explained in 5 episodes
Trace — 1× in this paper · explained in 2 episodes

Summary

A hydrodynamical description of isolated spherical voids in modified gravity (MG) extends standard General Relativity and dynamical dark energy treatments by encoding gravity modifications into effective couplings, yielding a compact non-linear evolution equation for Eulerian density contrast and providing a direct map between model functions and void observables.

The gist

We present a hydrodynamical description of isolated spherical voids 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.

The hydrodynamical approach

The framework is formulated in the Newtonian gauge for scalar perturbations of a spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) metric, assuming spherical symmetry, pressureless matter, and dark energy as a smooth background component. The evolution of the Eulerian density contrast is governed by equations that generalize the standard GR evolution equation. For modified gravity models (MG), these equations are modified through two functions, µNL and ΣNL, which generalize the Poisson and lensing equations:

∇2xΨ = 4πGa2ρ¯m µNL(a, x) δE
∇2x(Φ + Ψ) = 8πGa2ρ¯m ΣNL(a, x) δE

The void evolution equation is modified only through the gravitational source term, which becomes proportional to the effective coupling:

δ′′ E + (1 + δE) − 3/2omegam µNL(a, R) (1 + δE) δE = 0

Modified gravity model framework

The paper focuses on the luminal Galileon class of models, where derivative self-interactions generate Vainshtein screening. The modification to the gravitational coupling at linear scales is denoted by µL(a, R), and the non-linear modification is given by µNL(a, R). The effective gravitational coupling in the non-linear regime is expressed as:

µNL(a, R) = M2pl/M2 (1 + 2 / [2M2pl/µL − 1] R V cubed s / (1 + R V/R3 − 1))

The Vainshtein scale, r3V(r), is defined as r3V(r) = 8G β2λ2 m(r), where m(r) is the enclosed defect mass contrast. This scale dictates the screening mechanism, which is responsible for regulating the non-linear term proportional to λ2.

Void evolution and viability

The framework incorporates a void-informed viability requirement that translates into bounds on the theory parameter space and void depth. This criterion ensures that voids always lie in an unscreened regime on the physical branch, avoiding an imaginary fifth force:

The condition is enforced by requiring 1 + fMG(a) δE ≥ 0, where fMG(a) = 32π/3G β2λ2ρ¯m.
This yields a redshift-dependent minimum allowed void depth: δmin(z) = max[-1, -1/fMG(z)].

Lagrangian to Eulerian mapping and shell-crossing

A key component is the mapping between Lagrangian space (initial conditions) and Eulerian space (observables). The map is defined as δv(z, δE), which returns the linearly extrapolated value of the density contrast. The paper quantifies this sensitivity using relative percentage differences:

∆δv[%] = [δ model v(z, δE) − δ w0waCDM v(z, δE)] / [δ w0waCDM v (z, δE)] × 100.

The shell-crossing condition is defined as the time at which the outermost void shell reaches the surrounding environment: dδE/dδv,in = -(1 + δE)(1 + δv,in) δv,in. The analysis compares MG and GR thresholds with respect to w0waCDM and EdS references.

Diagnostics for breakdown

Three diagnostics are introduced to distinguish between shell-crossing breakdown and pathological branch onset:

δmin,p(z): The most negative density contrast reachable at redshift z by solving the equations while ignoring shell-crossing, under the requirement that the solution remains real and never enters the pathological regime.
δmin,h(z): The larger value between the shell-crossing bound and δmin,p.

Improvements for AI systems

As a fastidious and diligent researcher, I have analyzed this paper on Cosmic voids evolution in modified gravity via hydrodynamics. The core contribution lies in developing a self-consistent hydrodynamic framework to predict void dynamics across modified gravity (MG) models, specifically focusing on the implications of derivative self-interactions like Vainshtein screening.

Here are the specific improvements for AI systems and what those improved systems can achieve:

)1. Enhanced Physics-Informed Neural Networks (PINNs) for Non-Linear Cosmology

The paper provides a closed, non-linear evolution equation (Eq. 2.10 in MG, Eq. 2.6 in GR).

• Improvement: Develop PINNs specifically trained on this system to solve the Eulerian density contrast evolution across various MG parameter spaces (e.g., varying the braiding parameter αB0 and model function m).

• Capability: These AI systems can rapidly calculate the non-linear evolution of void profiles, including Lagrangian-to-Eulerian mapping and shell-crossing thresholds, for any given theoretical MG theory without requiring extensive numerical integration. They can instantly predict how a specific modification to the gravitational coupling (e.g., increasing αB0) shifts the void density profile or changes when shell-crossing occurs relative to GR.

)2. Automated Screening and Viability Constraint Engine

The paper introduces a void-informed viability requirement (Eq. 3.21: avoiding an imaginary fifth force).

• Improvement: Implement an AI module that continuously monitors the effective gravitational coupling function, specifically calculating the auxiliary function g(˜y) (Eq. 4.1) and checking if it enters the pathological regime where the square root argument becomes imaginary (i.e., when fMGδE < -1).

• Capability: This system acts as an automated theoretical filter. When presented with a set of MG parameters, it can instantly flag models that are theoretically inconsistent (i.e., those excluded by the void-informed bound), effectively pruning the parameter space for further analysis, which is crucial for high-dimensional model comparison.

)3. Lagrangian-to-Eulerian Mapping Predictor

The paper provides a map between Lagrangian space and Eulerian space (Eq. 4.8).

• Improvement: Train a neural network to learn this mapping from simulated or analytical solutions across different MG models, using the ICs specified in Section 2.3 as inputs and the final density contrast as output.

• Capability: This AI can instantly translate an initial underdense patch (Lagrangian space) into its predicted late-time observable state (Eulerian space, like void radius or density profile) for any MG model, significantly accelerating the interpretation of observational data from surveys like DESI or Euclid.

)4. Diagnostic Threshold Classifier

The paper defines three diagnostic thresholds: δmin,p(z), δmin,h(z), and δmin,p0(z).

• Improvement: Create a classification system that takes the output of the PINN (from point 1) and classifies the breakdown mechanism.

• Capability: The AI can determine whether a void evolution terminates due to shell-crossing (GR-like failure) or due to the onset of an imaginary force (MG pathology). This allows researchers to distinguish between these two physical failure modes, which is vital for correctly interpreting numerical simulations and theoretical predictions in the context of MG.

)5. Comparative Deviation Analyzer

The paper quantifies deviations from GR using metrics like ∆δE[%] and ∆µ[%].

• Improvement: Build a comparative analysis AI that takes the evolution trajectories (or final states) from multiple MG models and compares them directly against a baseline w0waCDM reference.

• Capability: This system can quantify the sensitivity of void observables to specific MG parameters. It can immediately tell researchers whether an observed deviation in void depth is more sensitive to the braiding parameter αB0 or the time-evolution parameter m, providing a direct guide for which modification to focus on when interpreting observational data.

These improvements transform AI from a mere calculator into a powerful, physics-aware modeling and diagnostic tool capable of exploring complex modified gravity parameter spaces with unprecedented speed and theoretical rigor.