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arxiv: 2605.03007 · v1 · submitted 2026-05-04 · 🌌 astro-ph.CO · hep-ph

Recognition: 2 theorem links

· Lean Theorem

Post-Recombination Fluctuations from a Sequestered Dark Sector

Salvatore Bottaro , Michael Geller , Diego Redigolo , Maya Tsur
Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:45 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-ph
keywords cosmic microwave backgrounddark sectorphase transitionsintegrated Sachs-Wolfe effectanisotropic stresscosmological perturbationspost-recombination fluctuationsenergy injection
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The pith

Late-time energy injections from a sequestered dark sector modify photon geodesics and leave imprints on the CMB dominated by anisotropic stress.

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

The paper develops a general formalism for the effects of brief energy releases after recombination on cosmic microwave background photons, relying only on the assumption that these releases happen much faster than the horizon scale. It derives how scalar, vector, and tensor perturbations alter photon paths and produce an integrated Sachs-Wolfe signal, finding that instantaneous anisotropic stress dominates the resulting temperature fluctuations. The authors apply this to first-order phase transitions in a hidden dark sector and conclude that existing observations already bound any fractional energy injection at the one-part-in-a-thousand level. A sympathetic reader cares because the method supplies a largely model-independent probe of otherwise invisible late-time physics. If the formalism is correct, many sequestered dark sector models face direct observational limits from CMB data.

Core claim

We develop a formalism to characterize the imprints of late-time sources of cosmological fluctuations under the sole assumption that the injection occurs on timescales short compared to the horizon. For post-recombination injections, we derive the general modification of photon geodesics in the presence of scalar, vector, and tensor perturbations, and compute the resulting impact on the Cosmic Microwave Background through the integrated Sachs-Wolfe effect. We show that the signal is generically dominated by instantaneous injections of anisotropic stress. As an application, we consider first-order phase transitions in a sequestered dark sector and show that current observations constrain the

What carries the argument

General modification of photon geodesics from scalar, vector, and tensor perturbations induced by short-timescale post-recombination energy injections, with the dominant contribution arising from instantaneous anisotropic stress.

If this is right

  • The CMB temperature anisotropy gains an extra integrated Sachs-Wolfe contribution from the induced perturbations.
  • The effect is generically dominated by anisotropic stress, while vector and tensor modes remain subdominant.
  • First-order phase transitions in sequestered dark sectors are limited to fractional energy injections below the permille level by current data.
  • The formalism applies to any post-recombination fluctuation source that satisfies the short-timescale condition.

Where Pith is reading between the lines

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

  • The same geodesic modification could be adapted to bound other late-time processes such as dark matter decays or late-time energy releases from new physics.
  • Future high-sensitivity CMB polarization data might better separate vector and tensor contributions from the dominant scalar anisotropic stress signal.
  • Analogous calculations could probe pre-recombination injections through different observables like the 21 cm signal or spectral distortions.

Load-bearing premise

The energy injection occurs on timescales short compared to the cosmological horizon at the relevant epoch.

What would settle it

CMB power spectrum measurements that show no excess temperature anisotropy at the amplitude predicted for a fractional energy injection of order 0.001 would directly challenge the derived constraints.

Figures

Figures reproduced from arXiv: 2605.03007 by Diego Redigolo, Maya Tsur, Michael Geller, Salvatore Bottaro.

Figure 1
Figure 1. Figure 1: FIG. 1: Cartoon of our setup where a DS which view at source ↗
Figure 2
Figure 2. Figure 2: To constrain the signal, we compare the χ 2 of the Dℓ measured by Planck5 assuming the ΛCDM fit with that where the PT signal is added. We then esti￾mate the 95% CL exclusion limit on ΩDS by requiring ∆χ 2 = χ 2 (ΛCDM + PT) − χ 2 (ΛCDM) ≃ 2.71. The re￾sults are shown in the right panel of view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Pressure ( view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Green’s functions view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Comparison of the relative contributions to the CMB angular power spectrum arising from the different view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Dimensionless power spectrum of the anisotropic stress, in the dimensionless units defined in Eq. ( view at source ↗
read the original abstract

We develop a formalism to characterize the imprints of late-time sources of cosmological fluctuations under the sole assumption that the injection occurs on timescales short compared to the horizon. For post-recombination injections, we derive the general modification of photon geodesics in the presence of scalar, vector, and tensor perturbations, and compute the resulting impact on the Cosmic Microwave Background through the integrated Sachs-Wolfe effect. We show that the signal is generically dominated by instantaneous injections of anisotropic stress. As an application, we consider first-order phase transitions in a sequestered dark sector and show that current observations constrain fractional energy injections at the permille level.

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

1 major / 1 minor

Summary. The manuscript develops a formalism to characterize the imprints of late-time sources of cosmological fluctuations under the sole assumption that the injection occurs on timescales short compared to the horizon. For post-recombination injections, it derives the general modification of photon geodesics in the presence of scalar, vector, and tensor perturbations and computes the resulting impact on the Cosmic Microwave Background through the integrated Sachs-Wolfe effect. The authors show that the signal is generically dominated by instantaneous injections of anisotropic stress. As an application, they consider first-order phase transitions in a sequestered dark sector and derive constraints on fractional energy injections at the permille level from current observations.

Significance. If the central claims hold, this provides a useful general framework for constraining late-time energy injections from dark sectors via CMB observations, with the minimal short-timescale assumption enabling broad applicability. The derivation of geodesic modifications across perturbation types and the concrete permille-level bounds on sequestered phase transitions are strengths that could inform future probes of hidden sectors. No machine-checked proofs or fully parameter-free derivations are highlighted, but the general formalism under a single external assumption is a positive feature.

major comments (1)
  1. [Abstract] Abstract and the section deriving the ISW effect: the claim that the signal is generically dominated by instantaneous injections of anisotropic stress follows from the short-timescale assumption alone. However, the integrated Sachs-Wolfe integral receives contributions from scalar density perturbations and vector velocity terms in addition to tensor anisotropic stress; the timescale condition permits an instantaneous treatment but does not suppress the former relative to the latter without further restrictions on the stress-energy tensor (e.g., tracelessness or vanishing isotropic pressure perturbations). This is load-bearing for the generic-domination statement and the subsequent observational constraints.
minor comments (1)
  1. The term 'sequestered dark sector' is introduced without a concise definition or reference to prior literature in the opening paragraphs; a brief explanatory sentence would improve accessibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address the major comment below, providing clarification on the assumptions underlying our claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract and the section deriving the ISW effect: the claim that the signal is generically dominated by instantaneous injections of anisotropic stress follows from the short-timescale assumption alone. However, the integrated Sachs-Wolfe integral receives contributions from scalar density perturbations and vector velocity terms in addition to tensor anisotropic stress; the timescale condition permits an instantaneous treatment but does not suppress the former relative to the latter without further restrictions on the stress-energy tensor (e.g., tracelessness or vanishing isotropic pressure perturbations). This is load-bearing for the generic-domination statement and the subsequent observational constraints.

    Authors: We thank the referee for highlighting this important nuance. The short-timescale assumption indeed enables the instantaneous approximation for the injection, allowing us to model the perturbations as occurring at a specific conformal time. However, the generic domination by anisotropic stress arises in our framework because we consider injections from a sequestered dark sector, where the stress-energy tensor perturbations are dominated by anisotropic stress (e.g., from bubble walls in phase transitions, which are traceless and have no isotropic pressure component in the relevant gauge). Scalar density and vector velocity contributions are subdominant under these conditions, as the dark sector does not source direct density perturbations in the visible sector without coupling. We have revised the abstract and the relevant section to explicitly state the additional assumptions on the stress-energy tensor that lead to this domination. This clarification strengthens the presentation without altering the derived constraints, which apply specifically to the phase transition scenario considered. revision: yes

Circularity Check

0 steps flagged

No circularity; formalism built from standard perturbation theory and external short-timescale assumption

full rationale

The paper states it develops the formalism under the sole external assumption of short-timescale injections relative to the horizon. It then derives the general photon geodesic modifications for scalar/vector/tensor perturbations and the ISW impact directly from those equations. No quoted step reduces a prediction to a fitted input, renames a known result, or relies on a load-bearing self-citation whose content is itself unverified or defined by the present work. The central claim of generic domination by anisotropic stress is presented as following from the general equations rather than being presupposed by definition or prior self-work. The derivation chain is therefore self-contained against external benchmarks of cosmological perturbation theory.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the short-timescale injection assumption and standard cosmological perturbation theory for photon geodesics and the integrated Sachs-Wolfe effect; the sequestered dark sector is an application example.

axioms (1)
  • domain assumption Injection occurs on timescales short compared to the horizon
    Explicitly stated as the sole assumption enabling the formalism for post-recombination injections.
invented entities (1)
  • Sequestered dark sector no independent evidence
    purpose: Hidden sector undergoing first-order phase transitions as an application of the formalism
    Introduced as the example model for constraining fractional energy injections; no independent evidence provided.

pith-pipeline@v0.9.0 · 5402 in / 1407 out tokens · 97190 ms · 2026-05-08T17:45:06.767455+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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Reference graph

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