arxiv: 2604.17383 · v1 · submitted 2026-04-19 · ✦ hep-ph · astro-ph.CO· hep-th

Recognition: unknown

Hydrodynamics of Filtered Dark Matter: A Two-Component Approach

Juntaro Wada

Authors on Pith no claims yet

Pith reviewed 2026-05-10 05:47 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COhep-th

keywords filtered dark matterfirst-order phase transitionhydrodynamicstwo-component fluidrelic abundanceballistic regimelocal thermal equilibriumdeflagration

0 comments

The pith

Modeling Filtered Dark Matter and radiation as separate fluids produces distinct hydrodynamic solutions with a shifted relic abundance.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets up the hydrodynamics of Filtered Dark Matter during a first-order phase transition as a two-component fluid because the bubble wall reflects dark matter particles while letting radiation pass through. In the ballistic regime the excluded dark matter energy-momentum forms a reflected mode, whereas in local thermal equilibrium it merges into the radiation fluid. This difference in how the excluded component is handled produces independent evolution for the dark matter and radiation fluids and changes the conditions under which deflagration-like solutions can exist. The resulting hydrodynamic effects alter the final relic abundance of dark matter compared with calculations that ignore the two-fluid distinction.

Core claim

The difference in the fate of the DM fluid that cannot enter the interior of the wall leads to different hydrodynamic behaviors in the DM and radiation fluids independently and, in particular, results in different existence conditions for solutions in the deflagration-like branch. Based on these results, the impact of hydrodynamic effects on the relic abundance of Filtered DM is revisited and a change in the abundance induced by hydrodynamic effects is demonstrated.

What carries the argument

Two-component fluid equations for dark matter and radiation with a reflective boundary condition applied only to the dark matter component.

If this is right

Solutions fall into detonation-like and deflagration-like branches in both the ballistic regime and the local thermal equilibrium regime.
Existence conditions for deflagration-like solutions differ between the two regimes because of how excluded dark matter energy-momentum is treated.
Hydrodynamic effects produce a measurable shift in the calculated relic abundance of Filtered Dark Matter.
The entropy current is not conserved in the two-fluid description.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The non-conservation of entropy in the two-fluid system may require revised entropy accounting when computing gravitational-wave signals from the same phase transition.
The approach could be applied to other dark-sector models in which only a subset of particles interacts strongly with the bubble wall.
Changes in relic abundance from these hydrodynamic effects would tighten or relax existing cosmological bounds on the Filtered Dark Matter parameter space.

Load-bearing premise

The bubble wall is highly reflective of the dark matter fluid but transparent to radiation.

What would settle it

Numerical integration of the two-fluid hydrodynamic equations that either confirms or rules out the predicted difference in deflagration-like solution existence between the ballistic and local thermal equilibrium regimes.

Figures

Figures reproduced from arXiv: 2604.17383 by Juntaro Wada.

**Figure 2.** Figure 2: FIG. 2. Schematic illustration of the variables: the temper [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Velocity dependence of the coefficient characterizing [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. The relation between the DM fluid velocities inside and outside the wall obtained from the matching conditions. The [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. The impact of hydrodynamics on the DM abundance [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. The relation between the DM fluid velocities inside and outside the wall obtained from the matching conditions [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗

read the original abstract

We study the hydrodynamics of the Filtered Dark Matter (Filtered DM) scenario during a first-order phase transition (FOPT). In this scenario, the bubble wall is highly reflective of the dark matter (DM) fluid but transparent to radiation, making the hydrodynamic problem fundamentally different from that of the electroweak FOPT. Motivated by this property, we formulate the hydrodynamics of this system as a two-component fluid composed of DM and radiation, and find that the solutions can be classified into detonation-like and deflagration-like branches in the ballistic regime and in the local thermal equilibrium (LTE) regime. In the ballistic regime, the energy--momentum of DM that cannot enter the wall appears as a reflected mode, while in the LTE regime, it relaxes into the energy--momentum of radiation. We find that this difference in the fate of the DM fluid that cannot enter the interior of the wall leads to different hydrodynamic behaviors in the DM and radiation fluids independently and, in particular, results in different existence conditions for solutions in the deflagration-like branch. Based on these results, we further revisit the impact of hydrodynamic effects on the relic abundance of Filtered DM and demonstrate the change in the abundance induced by hydrodynamic effects. In addition, we also discuss the non-conservation of the entropy current from the viewpoint of the two-fluid system, and briefly comment on the similarity between the Filtered DM system and information-thermodynamic systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper introduces a two-component hydro model for filtered DM that splits DM and radiation behaviors by ballistic vs LTE regime and changes deflagration conditions plus relic abundance.

read the letter

The main takeaway is a two-component fluid treatment for Filtered Dark Matter during first-order phase transitions. The bubble wall reflects DM but passes radiation, so the fluids are modeled separately and their solutions split into ballistic and LTE regimes with different outcomes for the DM that cannot cross the wall. In the ballistic case the reflected energy-momentum stays as a distinct mode; in LTE it relaxes into the radiation fluid. This produces independent hydrodynamic evolution and shifts the existence conditions for deflagration-like solutions, which in turn alters the relic abundance estimate. The paper also notes entropy-current non-conservation in the two-fluid system and draws a brief parallel to information-thermodynamic setups. What the work does cleanly is take the wall-reflectivity property as given and work out its hydrodynamic consequences without forcing the system back into single-fluid language. The logic from the stated distinction to the changed deflagration branch follows directly, and the stress-test finds no internal contradiction. The soft spots are modest but real. The central results rest on the high DM reflectivity assumption, which is motivated but would benefit from more discussion of its parameter range or microphysical origin. The abstract claims a change in relic abundance without showing the size of the shift or direct comparison to prior single-fluid results, so the practical impact is still unclear. Derivations are not visible here, though nothing in the outline suggests circularity or invented entities. This is for people already working on dark-matter production during phase transitions or on gravitational-wave signals from first-order transitions. The modeling choice is specific enough to be worth checking in detail. I would send it to peer review; the framework is new enough and the logic tight enough that referees can usefully test the equations and the quantitative relic shift.

Referee Report

0 major / 3 minor

Summary. The paper develops a two-component hydrodynamic description (DM plus radiation) for the Filtered Dark Matter scenario during a first-order phase transition. Because the bubble wall is taken to be reflective for DM but transparent to radiation, the system is treated separately in the ballistic regime (where reflected DM appears as a distinct mode) and the local thermal equilibrium regime (where reflected DM relaxes into the radiation fluid). Solutions are classified into detonation-like and deflagration-like branches; the different fate of the excluded DM fluid is shown to produce distinct hydrodynamic profiles and, in particular, different existence conditions for the deflagration-like branch. The work then re-examines the effect of these hydrodynamics on the DM relic abundance and comments on the non-conservation of the entropy current together with an analogy to information-thermodynamic systems.

Significance. If the derivations hold, the manuscript supplies a tailored hydrodynamic framework that captures the distinctive wall-interaction properties of Filtered DM, thereby refining relic-density predictions in this class of models. The explicit separation of ballistic and LTE regimes and the resulting shift in deflagration existence conditions constitute a concrete, falsifiable advance over single-fluid treatments of electroweak-scale transitions.

minor comments (3)

[Introduction / §2] The abstract and introduction introduce the two-component classification but do not state the explicit matching conditions (velocity and energy-momentum continuity) used at the wall; adding a short paragraph or equation block early in the text would clarify the setup for readers.
[Relic abundance section] In the relic-abundance discussion, the quantitative shift induced by the hydrodynamic treatment is described qualitatively; a brief table or plot comparing the new abundance to the standard (no-hydro) result would strengthen the claim.
[Final discussion] The analogy to information-thermodynamic systems is mentioned only in passing; a single sentence linking the non-conservation of the entropy current to a specific information-theoretic quantity would make the parallel more concrete.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work on the two-component hydrodynamics of Filtered Dark Matter and for recommending minor revision. The summary accurately captures the distinction between ballistic and LTE regimes and the resulting impact on deflagration-like solutions and relic abundance. No major comments requiring point-by-point rebuttal were raised.

Circularity Check

0 steps flagged

No significant circularity; derivation applies standard hydrodynamics to stated two-fluid setup

full rationale

The paper's core steps consist of (1) adopting the given physical distinction that the bubble wall reflects DM but transmits radiation, (2) writing the two-component hydrodynamic equations for DM and radiation fluids separately in the ballistic and LTE regimes, and (3) classifying solutions into detonation-like and deflagration-like branches while noting the different fate of reflected DM energy-momentum. These steps follow directly from the stated boundary conditions and standard conservation laws; no equation is defined in terms of its own output, no fitted parameter is relabeled as a prediction, and no load-bearing premise rests on a self-citation chain. The subsequent relic-abundance discussion and entropy-current remark are presented as consequences of the same hydrodynamic classification rather than inputs. The derivation therefore remains self-contained against external hydrodynamic principles.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard multi-fluid relativistic hydrodynamics plus the domain-specific assumption of differential wall reflectivity. No free parameters, invented entities, or additional axioms are identifiable from the abstract alone.

axioms (2)

standard math Relativistic hydrodynamic equations govern the two-component (DM + radiation) fluid
Invoked to classify detonation-like and deflagration-like solutions in ballistic and LTE regimes.
domain assumption Bubble wall is highly reflective to DM fluid but transparent to radiation
This property is stated as the motivation for the two-component formulation and the difference from electroweak FOPT.

pith-pipeline@v0.9.0 · 5556 in / 1273 out tokens · 60220 ms · 2026-05-10T05:47:11.210569+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Solution in Ballistic Regime The equations to be solved, Eqs. (49) and (50), can be rewritten as ˜ωout χ,f(γout χ,f)2vout χ,f −ω in χ,f(γin χ,f)2vin χ,f = 0 (61) ˜ωout χ,f(γout χ,f)2(vout χ,f)2 −ω in χ,f(γin χ,f)2(vin χ,f)2 =p in χ,f −˜pout χ,f + ∆ϵeff,r χ ,(62) where we have introduced the following parameters: ˜ωout χ,f = ˜ρout χ,f + ˜pout χ,f ,(63) ˜ρo...
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Friction in Ballistic Regime In determining the wall velocity, an important condi- tion is the balance between the driving force, given by the difference in the effective potential across the wall, and the backreaction (friction) exerted by the surround- ing fluid. In the ballistic regime, as already studied in the literature [29, 30, 47], the reflected c...
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Solution in LTE Regime The set of equations to be solved, Eqs. (90)-(93), can be rewritten as follows: ¯ωout χ,f(γout χ,f)2vout χ,f −ω in χ,f(γin χ,f)2vin χ,f = 0,(103) ¯ωout χ,f(γout χ,f)2(vout χ,f)2 −ω in χ,f(γin χ,f)2(vin χ,f)2 =p in χ,f −¯pout χ,f + ∆ϵeff,t χ,f ,(104) ¯ωout rad(γout rad)2vout rad −ω in rad(γin rad)2vin rad = 0,(105) ¯ωout rad(γout rad...
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