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arxiv: 2606.12521 · v1 · pith:B4UGRXG2new · submitted 2026-06-10 · 🌌 astro-ph.CO

Dark Matter with a Drag at Low Redshift

Martin Schmaltz , Eashwar N. Sivarajan This is my paper

Pith reviewed 2026-06-27 08:37 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords dark matterdark radiationdecaying dark matterstructure growthf sigma8cosmological modellate-time interactions
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The pith

Dark matter that decays into radiation at late times experiences a drag force that slows the growth of cosmic structures at low redshifts.

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

The paper constructs particle models where dark matter interacts with dark radiation produced from its own decay, creating a drag that increases at late times. This suppresses the linear growth rate of large scale structure below the predictions of LambdaCDM while leaving the background expansion, Big Bang nucleosynthesis, and primary cosmic microwave background signals unchanged. An explicit iDCDM model adds only two parameters and shows a modest preference in fits to current f sigma8 data. The model predicts a distinctive step-shaped suppression in the growth rate that can be tested by future surveys.

Core claim

An explicit interacting Decaying Cold Dark Matter (iDCDM) model adds two parameters beyond LambdaCDM while leaving the background, BBN, and primary CMB intact. It predicts a step-shaped suppression of the linear growth rate f(k,z) and shows a modest preference over LambdaCDM with Delta chi squared between -2.7 and -7.6 when confronted with current f sigma8 data.

What carries the argument

The iDCDM model where dark matter decays to produce dark radiation that exerts a drag force on the remaining dark matter, with the interaction strength growing at late times.

If this is right

  • The growth rate f(k,z) is suppressed in a step shape at low redshifts.
  • Current f sigma8 data is fit better than LambdaCDM by Delta chi^2 of -2.7 to -7.6.
  • Early universe observables like BBN and primary CMB are unaffected.
  • Future k- and z-resolved measurements from DESI, Euclid, and Rubin will provide decisive tests.

Where Pith is reading between the lines

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

  • If the drag is confirmed, it could explain the growth tension without new early-universe physics.
  • The late-time production of dark radiation might have observable effects in other cosmological probes if the decay products are detectable.
  • Extensions could explore different redshift scalings of the drag to optimize fits.

Load-bearing premise

The radiation that interacts with dark matter is produced at late times from dark matter decay, allowing the drag to grow with redshift without changing early-universe observables.

What would settle it

A high-precision measurement of the growth rate f sigma8 at low redshifts showing no improvement in fit or the absence of the predicted step-shaped suppression in f(k,z).

Figures

Figures reproduced from arXiv: 2606.12521 by Eashwar N. Sivarajan, Martin Schmaltz.

Figure 1
Figure 1. Figure 1: B. Summary of effective cosmological description At the cosmological level, the UV model reduces to a two-component dark sector with DM and DR. The DM [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Profile likelihood scan comparing the standard [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Ratio of the best-fit iDCDM linear matter [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Two-dimensional marginalized posterior [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: One-dimensional marginalized posterior [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Verification of the analytical approximation [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: One-dimensional marginalized posterior distri [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Two-dimensional marginalized posterior contours (68% and 95% C.L.) and one-dimensional marginalized [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: shows the profile of the total ∆χ 2 versus log10(Γd/Γs). With the standard fσ8 likelihood, the pro￾file decreases past the cap at −2.5, indicating that the data would prefer a step at still larger kd if we allowed it. We hold the cap because past −2.5 the standard fσ8 like￾lihood is no longer a faithful translation of P(k) to the ob￾servable ( [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
read the original abstract

Recent analyses of $f\sigma_8$ and weak-lensing data indicate that the linear growth rate at $z\lesssim 1$ may be lower than predicted by $\Lambda$CDM. This motivates models of dark matter in which large scale structure growth slows relative to $\Lambda$CDM at late times. We construct particle models in which dark matter experiences a drag with dark radiation that grows at late times, unlike conventional DM--DR interactions, which fade as the universe expands. A key ingredient is that the radiation interacting with the dark matter is produced at late times from dark matter decay. An explicit model, interacting Decaying Cold Dark Matter (iDCDM), adds two parameters beyond $\Lambda$CDM while leaving the background, BBN, and primary CMB intact. But it predicts a step-shaped suppression of the linear growth rate $f(k,z)$, a distinctive target for DESI, Euclid, and Rubin. Confronted with current data, iDCDM shows a modest preference over $\Lambda$CDM, driven by $f\sigma_8$, with $\Delta\chi^2$ between $-2.7$ and $-7.6$ depending on the assumed scaling of the drag with redshift and on neutrino masses. The decisive test will come from upcoming $k$- and $z$-resolved growth measurements.

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.

Referee Report

2 major / 1 minor

Summary. The paper proposes an interacting Decaying Cold Dark Matter (iDCDM) model with two additional free parameters (decay rate and drag coupling strength) beyond ΛCDM. Dark matter decays at late times into dark radiation that interacts with the remaining DM, producing a redshift-growing drag that suppresses the linear growth rate f(k,z) in a step-like manner at z≲1. The model is constructed to leave the background expansion, BBN, and primary CMB unchanged, and is shown to yield Δχ² improvements of -2.7 to -7.6 over ΛCDM when fit to current fσ8 data, with the preference depending on the assumed drag scaling and neutrino masses. Distinctive predictions are made for future k- and z-resolved growth measurements from DESI, Euclid, and Rubin.

Significance. If the central construction holds—that late-time DM decay can source interacting DR yielding a growing drag without perturbing early-universe observables—the model offers a particle-physics-motivated mechanism for late-time growth suppression with a distinctive step-shaped signature. This would be a substantive addition to the literature on growth-rate tensions, providing falsifiable targets for upcoming surveys. The modest data preference and explicit two-parameter extension are strengths, though the result's robustness hinges on the unshown early-universe decoupling.

major comments (2)
  1. [abstract and model-construction paragraph] Abstract and model-construction paragraph: The claim that the model 'leaves the background, BBN, and primary CMB intact' is load-bearing for the central assertion of a late-time-only effect, yet no explicit derivation, perturbation equations, or numerical checks are referenced showing that the decay products and chosen interaction-rate scaling leave the sound horizon, baryon loading, and pre-recombination evolution unaltered. Without these, the separation between early and late physics cannot be verified.
  2. [data-confrontation section] Data-confrontation section (implied by the reported Δχ² values): The preference over ΛCDM (Δχ² between -2.7 and -7.6) is stated to depend on the assumed scaling of the drag with redshift and on neutrino masses; because the two free parameters are fitted directly to the same fσ8 data used to claim the improvement, the step-shaped suppression feature is not an independent prediction but is tied to the fit, weakening the claim of a 'modest preference' as a genuine model advantage.
minor comments (1)
  1. [abstract] The abstract refers to 'the assumed dr' without defining the acronym on first use; expand to 'dark radiation' for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We respond point-by-point to the major comments below. We agree that additional explicit checks on the early-universe behavior will strengthen the paper and plan to incorporate them.

read point-by-point responses

  1. Referee: [abstract and model-construction paragraph] Abstract and model-construction paragraph: The claim that the model 'leaves the background, BBN, and primary CMB intact' is load-bearing for the central assertion of a late-time-only effect, yet no explicit derivation, perturbation equations, or numerical checks are referenced showing that the decay products and chosen interaction-rate scaling leave the sound horizon, baryon loading, and pre-recombination evolution unaltered. Without these, the separation between early and late physics cannot be verified.

    Authors: We agree that the manuscript would benefit from explicit verification. The model is constructed so that the decay rate is negligible prior to recombination (due to the redshift dependence of the decay and interaction terms), leaving the background expansion, sound horizon, and pre-recombination evolution identical to ΛCDM. To address the concern, we will add an appendix containing the relevant perturbation equations and a brief demonstration (via modified Boltzmann code output) that the CMB power spectra and BBN abundances remain unchanged at the level of current precision. revision: yes

  2. Referee: [data-confrontation section] Data-confrontation section (implied by the reported Δχ² values): The preference over ΛCDM (Δχ² between -2.7 and -7.6) is stated to depend on the assumed scaling of the drag with redshift and on neutrino masses; because the two free parameters are fitted directly to the same fσ8 data used to claim the improvement, the step-shaped suppression feature is not an independent prediction but is tied to the fit, weakening the claim of a 'modest preference' as a genuine model advantage.

    Authors: The two additional parameters set the amplitude and the characteristic redshift at which the drag becomes important, but the step-like functional form of the suppression in f(k,z) is fixed by the underlying physics: interacting dark radiation is sourced only at late times by DM decay, producing a drag that strengthens toward z=0. This shape is a genuine prediction of the construction rather than a free functional choice. The fit to fσ8 data then tests whether this physically motivated form improves the description relative to ΛCDM. We will add clarifying text in the data section to emphasize the distinction between the predicted shape and the fitted parameters. We therefore maintain that the reported preference reflects a genuine model advantage with a distinctive, falsifiable signature. revision: partial

Circularity Check

1 steps flagged

Two free parameters fitted to fσ8 data presented as independent prediction of step-shaped suppression

specific steps
  1. fitted input called prediction [Abstract]
    "An explicit model, interacting Decaying Cold Dark Matter (iDCDM), adds two parameters beyond ΛCDM while leaving the background, BBN, and primary CMB intact. But it predicts a step-shaped suppression of the linear growth rate f(k,z), a distinctive target for DESI, Euclid, and Rubin. Confronted with current data, iDCDM shows a modest preference over ΛCDM, driven by fσ8, with Δχ² between −2.7 and −7.6 depending on the assumed scaling of the drag with redshift and on neutrino masses."

    The two added parameters directly set the drag scaling and amplitude that produce the step-shaped suppression. The paper then fits those parameters to the fσ8 data set and reports the resulting Δχ² as evidence of preference; the distinctive shape is therefore the fitted output, not an independent prediction.

full rationale

The paper constructs iDCDM by adding two parameters that control the late-time DM-DR drag strength and redshift scaling. These parameters are varied to match the observed fσ8 suppression, yielding the quoted Δχ² improvement. The claimed 'prediction' of a step-shaped f(k,z) feature is therefore the direct output of the same fit, rather than an a priori consequence independent of the data used for the preference claim. No other circular steps (self-citation chains or definitional loops) are exhibited in the provided text.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central claim rests on two new free parameters controlling the decay rate and drag strength, plus the domain assumption that the produced radiation interacts only with dark matter and does not affect photons or baryons after recombination.

free parameters (2)
  • decay rate parameter
    Controls the timing and amount of dark radiation produced from dark matter decay; fitted to produce late-time drag.
  • drag coupling strength
    Sets the interaction strength between dark matter and the produced radiation; chosen to match the desired suppression scale.
axioms (1)
  • domain assumption Standard LambdaCDM background evolution and recombination physics remain valid when the new interaction is active only after recombination.
    Invoked to claim that BBN and primary CMB are left intact.
invented entities (1)
  • late-time produced dark radiation no independent evidence
    purpose: Source of the growing drag force on dark matter
    Postulated new radiation component generated by dark matter decay; no independent evidence provided beyond the model fit.

pith-pipeline@v0.9.1-grok · 5769 in / 1674 out tokens · 18424 ms · 2026-06-27T08:37:56.874129+00:00 · methodology

discussion (0)

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Reference graph

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    Light-particle thermalization The massless speciesψandγ d self-interact with various 2 to 2 processes whose momentum transfer rates scale like Γγγ ∼α 2 d Td ,Γ ψγ ∼α 2 d Td .(B1) Number-changing 2→3 processes (e.g. double Compton) carry a naive extraα d suppression, but an IR diver- gence from the massless fermion propagator, regulated 12 by a thermal Deb...

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