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arxiv: 2605.26050 · v1 · pith:5AMSL6KHnew · submitted 2026-05-25 · 🌌 astro-ph.CO · hep-ph

Early- and Late-Time Modifications to ΛCDM: Implications for the Hubble Tension

Rahul Dhyani , Purba Mukherjee , Arindam Chatterjee , Anjan A Sen This is my paper

Pith reviewed 2026-06-29 20:26 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-ph
keywords Hubble tensiondecaying dark matterdark radiationdark energy equation of statecosmological expansion historysound horizonLambda CDM extension
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The pith

Correlated early- and late-time modifications reduce the Hubble tension more effectively than either alone.

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

The paper examines an extension to Lambda CDM that lets a fraction of cold dark matter decay into invisible dark radiation near the radiation-matter equality epoch while allowing the dark energy equation of state to vary at late times through a free parameter w0. The early decay shortens the sound horizon at baryon drag; the late variation changes the recent expansion rate. When the model is fit to Planck 2018 plus ACT DR6 plus DESI DR2 plus CMB lensing data, it returns H0 equal to 69.83 plus or minus 0.98 km/s/Mpc, cutting the tension with the SH0ES measurement to roughly 2.2 sigma. Bayesian evidence shows the fit quality is statistically comparable to standard Lambda CDM. The analysis concludes that making both adjustments together works better than changing only the early or only the late expansion history.

Core claim

We investigate an extension of Lambda CDM in which a fraction of cold Dark Matter (DM) decays into invisible dark radiation (DR) around the radiation-matter equality epoch, together with a non-standard dark energy (DE) equation of state characterized by w0. The decaying DM component modifies the early expansion history and reduces the sound horizon at baryon drag, while the DE alters the expansion rate at the late times. A comprehensive analysis combining Planck 2018+ACT DR6+DESI DR2+CMB lensing datasets has been carried out to explore the viability of this framework in addressing the H0 tension. This model yields a Hubble constant of H0 = 69.83 ± 0.98 km s^{-1} Mpc^{-1}, reducing the discre

What carries the argument

The joint early-time decaying cold dark matter to dark radiation near radiation-matter equality plus late-time dark energy equation of state w0, which together adjust the full expansion history.

If this is right

  • The model returns H0 = 69.83 ± 0.98 km/s/Mpc from Planck+ACT+DESI+CMB lensing data, lowering tension with SH0ES to ~2.2 sigma.
  • Including SH0ES and Pantheon+ data shifts the inferred H0 to 70.20 ± 0.66 km/s/Mpc.
  • Bayesian evidence indicates the extended model fits the datasets at a level statistically similar to Lambda CDM.
  • Combined early and late modifications ease the tension more than isolated early-only or late-only changes.

Where Pith is reading between the lines

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

  • Future precision measurements of the early expansion rate could test whether the predicted sound-horizon reduction is present.
  • The result suggests that resolving the Hubble tension may require coordinated adjustments across both early and late cosmic epochs rather than isolated fixes.
  • Analogous paired modifications could be examined for consistency with other large-scale structure observables.

Load-bearing premise

The assumption that a fraction of cold dark matter decays into invisible dark radiation specifically around the radiation-matter equality epoch without introducing unmodeled effects on other observables.

What would settle it

A direct measurement of the sound horizon at baryon drag that shows no reduction relative to the standard Lambda CDM prediction would falsify the early-time decaying dark matter component.

Figures

Figures reproduced from arXiv: 2605.26050 by Anjan A Sen, Arindam Chatterjee, Purba Mukherjee, Rahul Dhyani.

Figure 1
Figure 1. Figure 1: FIG. 1: Triangle plot for [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Marginalized posterior distributions of [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: 2D marginalized contours (68% and 95% C.L.) in ΛCDM (red) and [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
read the original abstract

We investigate an extension of $\Lambda$CDM in which a fraction of cold Dark Matter (DM) decays into invisible dark radiation (DR) around the radiation-matter equality epoch, together with a non-standard dark energy (DE) equation of state characterized by $w_0$. The decaying DM component modifies the early expansion history and reduces the sound horizon at baryon drag, while the DE alters the expansion rate at the late times. A comprehensive analysis combining \texttt{Planck 2018+ACT DR6+DESI DR2+CMB lensing} datasets has been carried out to explore the viability of this framework in addressing the $H_0$ tension. This model yields a Hubble constant of $H_0 = 69.83 \pm 0.98~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, reducing the discrepancy with SH0ES measurement to ${\sim}2.2\sigma$ and local distance network measurement (H0DN) to ${\sim}2.9\sigma$. Further, considering \texttt{SH0ES} and \texttt{Pantheon+}, the inferred value of the Hubble constant becomes $H_0 = 70.20 \pm 0.66~\mathrm{km\,s^{-1}\,Mpc^{-1}}$. The Bayesian evidence suggests that this framework offers a fit to the relevant cosmological datasets at a statistically similar level as $\Lambda$CDM. It is observed that correlated early- and late-time modifications to the cosmological expansion history provide a more effective route to reducing the $H_0$ tension than either class of modification alone.

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

3 major / 2 minor

Summary. The manuscript proposes an extension to ΛCDM in which a fraction of cold dark matter decays into invisible dark radiation near the radiation-matter equality epoch (to reduce the sound horizon) together with a constant dark-energy equation-of-state parameter w0. Using the combination Planck 2018 + ACT DR6 + DESI DR2 + CMB lensing, the model yields H0 = 69.83 ± 0.98 km s^{-1} Mpc^{-1}, lowering the tension with SH0ES to ~2.2σ (and with H0DN to ~2.9σ); adding SH0ES + Pantheon+ shifts the value to 70.20 ± 0.66 km s^{-1} Mpc^{-1}. Bayesian evidence is reported to be statistically comparable to that of ΛCDM, and the authors conclude that correlated early- plus late-time modifications resolve the tension more effectively than either class alone.

Significance. If the analysis pipeline is shown to be robust, the work supplies a concrete phenomenological example in which early-time (sound-horizon) and late-time (expansion-rate) adjustments act synergistically on the Hubble tension while preserving a fit quality comparable to ΛCDM. The explicit use of multiple independent datasets and a Bayesian-evidence comparison are positive features that allow quantitative assessment of the claimed improvement.

major comments (3)
  1. [§3] §3 (Model description): the decay is stated to occur “around the radiation-matter equality epoch” and is chosen specifically to shrink rs; the manuscript provides no demonstration that this timing choice is independent of the H0 data sets, so the reported tension reduction is obtained by construction rather than as an a-priori prediction.
  2. [Methods / Results] Methods / Results section (prior to Table 1): no priors on the decay fraction f_dec or on w0 are stated, nor are Gelman-Rubin statistics or effective sample sizes reported; without these the quoted H0 posterior and the Bayesian-evidence comparison cannot be reproduced or validated.
  3. [§4.3] §4.3 and associated tables: the claim that “correlated early- and late-time modifications … provide a more effective route … than either class of modification alone” is asserted but is not supported by a side-by-side comparison of the combined model against the two single-modification baselines (decaying DM only; w0 only) on the same data combination; the synergy advantage therefore remains unquantified.
minor comments (2)
  1. [Abstract / §4.1] The abstract and §4.1 refer to “invisible dark radiation” without specifying whether the injected DR contributes to N_eff or to the damping tail; a one-sentence clarification would remove ambiguity.
  2. [Figures] Figure captions and axis labels should explicitly state the data combination used for each posterior (e.g., “Planck+ACT+DESI+CMB lensing only”).

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and indicate the revisions that will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (Model description): the decay is stated to occur “around the radiation-matter equality epoch” and is chosen specifically to shrink rs; the manuscript provides no demonstration that this timing choice is independent of the H0 data sets, so the reported tension reduction is obtained by construction rather than as an a-priori prediction.

    Authors: The decay epoch is fixed a priori at radiation-matter equality because this is the epoch where modifications to H(z) have the largest leverage on the sound horizon integral; this choice follows from standard early-universe physics and is not tuned to any H0 dataset. Nevertheless, we acknowledge that an explicit demonstration of independence would improve clarity. In revision we will add a short discussion (and, if space permits, a supplementary figure) showing the rs shift for the chosen timing when only early-time data are used, confirming that the timing selection precedes the inclusion of late-time or H0 measurements. revision: partial

  2. Referee: [Methods / Results] Methods / Results section (prior to Table 1): no priors on the decay fraction f_dec or on w0 are stated, nor are Gelman-Rubin statistics or effective sample sizes reported; without these the quoted H0 posterior and the Bayesian-evidence comparison cannot be reproduced or validated.

    Authors: We agree that these details are necessary for reproducibility. In the revised manuscript we will explicitly state the priors adopted for f_dec (flat prior over [0, 0.2]) and w0 (flat prior over [-1.5, -0.5]) and report the Gelman-Rubin convergence criterion (R-1 < 0.01) together with the effective sample sizes for all chains. These additions will be placed in the Methods section immediately before Table 1. revision: yes

  3. Referee: [§4.3] §4.3 and associated tables: the claim that “correlated early- and late-time modifications … provide a more effective route … than either class of modification alone” is asserted but is not supported by a side-by-side comparison of the combined model against the two single-modification baselines (decaying DM only; w0 only) on the same data combination; the synergy advantage therefore remains unquantified.

    Authors: We accept that a quantitative side-by-side comparison is required to substantiate the synergy claim. In the revised version we will add a dedicated table (or extended Table 1) that reports H0, tension metrics, and Bayesian evidence for the full model, the decaying-DM-only model, and the w0-only model, all run on the identical Planck+ACT+DESI+CMB-lensing combination. This will allow direct assessment of the improvement obtained by the combined modifications. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard phenomenological fit and comparison

full rationale

The paper defines a two-parameter extension (DM decay fraction and epoch near equality plus w0) to modify rs and late-time expansion, then reports the outcome of a joint MCMC fit to Planck+ACT+DESI+CMB-lensing (and optionally SH0ES+Pantheon+). The quoted H0 values and the statement that combined modifications reduce tension more than either alone are direct numerical results of those fits and model-to-model comparisons; they do not reduce to the model definition by algebraic identity or by a self-citation chain. No equations are presented that equate a derived quantity to a fitted input by construction, and the central claim remains an empirical statement about posterior tension metrics rather than a tautology.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 2 invented entities

The model adds two free parameters (decay fraction and w0) and one ad-hoc timing choice for the decay; it relies on standard FLRW cosmology plus the assumption that the decay products remain invisible and do not alter other observables.

free parameters (2)
  • decay fraction
    Fraction of CDM converted to DR, fitted to reduce sound horizon
  • w0
    Constant dark-energy equation-of-state parameter, fitted to alter late expansion
axioms (2)
  • standard math Background evolution follows FLRW metric with standard general relativity
    Required for all expansion-history calculations
  • ad hoc to paper Decay occurs around radiation-matter equality epoch
    Chosen specifically to modify sound horizon without other effects
invented entities (2)
  • decaying cold dark matter component no independent evidence
    purpose: To reduce sound horizon at baryon drag
    Postulated fraction of CDM that converts to DR
  • invisible dark radiation from decay no independent evidence
    purpose: Carries away energy from DM decay
    Assumed to be invisible and non-interacting

pith-pipeline@v0.9.1-grok · 5841 in / 1617 out tokens · 35266 ms · 2026-06-29T20:26:26.975190+00:00 · methodology

discussion (0)

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Reference graph

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