arxiv: 2605.11956 · v1 · submitted 2026-05-12 · ✦ hep-ph · astro-ph.CO· gr-qc· hep-th

Recognition: no theorem link

Probing the small-scale primordial power spectrum via relic neutrinos and acoustic reheating

Giovanni Piccoli, Joseph Silk, Sunny Vagnozzi

Pith reviewed 2026-05-13 05:23 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COgr-qchep-th

keywords relic neutrinosprimordial power spectrumdiffusion dampingacoustic reheatingPTOLEMYneutrino temperaturesmall-scale perturbationsBig Bang nucleosynthesis

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The pith

Dissipation of small-scale primordial perturbations after neutrino decoupling lowers the present-day neutrino temperature and reduces relic neutrino abundance in proportion to the integrated curvature power spectrum.

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

The paper establishes that diffusion damping of small-scale cosmic perturbations injects energy into the photon-baryon plasma after neutrinos have decoupled. This extra heating raises the photon temperature without a corresponding increase for the neutrinos, resulting in a lower neutrino temperature today than the standard 1.96 K and a reduced relic neutrino abundance. The magnitude of the temperature drop is set by the integral of the primordial curvature power spectrum over the affected scales. A future detection of relic neutrinos by an experiment such as PTOLEMY could therefore translate into upper limits on that small-scale power. These limits would sit in a range of wavenumbers inaccessible to most other cosmological probes and would be complementary to constraints from Big Bang nucleosynthesis, spectral distortions, pulsar timing arrays, and future 21-cm observations.

Core claim

The dissipation of small-scale perturbations through diffusion damping after neutrino decoupling lowers the present-day neutrino temperature compared to the expected value of 1.96 K. This reduces the relic neutrino abundance by an amount controlled by the integral of the primordial curvature power spectrum Δ_R²(k). We find that a relic neutrino detection by PTOLEMY can set limits Δ_R²(k) ≲ O(0.1) on scales k ≲ 3 × 10^5 Mpc^{-1}, complementary to limits from Big Bang Nucleosynthesis, spectral distortions, pulsar timing arrays, and future dark ages 21-cm observations.

What carries the argument

Diffusion damping of acoustic perturbations in the early-universe plasma after neutrino decoupling, which transfers perturbation energy preferentially to the photon fluid and thereby suppresses the relic neutrino temperature and abundance in direct proportion to the integrated small-scale primordial curvature power spectrum.

If this is right

The size of the neutrino temperature reduction is fixed by the integral of Δ_R²(k) over the relevant small scales.
PTOLEMY could place constraints on primordial power at wavenumbers far smaller than those reached by the cosmic microwave background or large-scale structure surveys.
The resulting bounds would be independent of and complementary to existing limits from Big Bang nucleosynthesis and pulsar timing arrays.
Future dark-ages 21-cm observations could furnish similar but distinct constraints on the same small-scale power.

Where Pith is reading between the lines

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

Precise relic-neutrino temperature measurements could become a new probe of inflationary dynamics on scales many orders of magnitude smaller than the cosmic microwave background.
The same damping mechanism might alter expectations for the relic abundance of any other species that decouples before the damping epoch.
Comparing the neutrino-temperature effect with spectral-distortion limits could test the assumed timing of neutrino decoupling relative to the damping process.

Load-bearing premise

The assumption that diffusion damping after neutrino decoupling produces a lowering of the neutrino temperature whose magnitude is controlled solely by the integral of the primordial curvature power spectrum without significant confounding contributions from other processes or uncertainties in the decoupling epoch.

What would settle it

A PTOLEMY measurement of the relic neutrino temperature or capture rate that matches the standard 1.96 K expectation with no detectable reduction would falsify the existence of substantial small-scale primordial power under the diffusion-damping scenario.

Figures

Figures reproduced from arXiv: 2605.11956 by Giovanni Piccoli, Joseph Silk, Sunny Vagnozzi.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

read the original abstract

We show that the dissipation of small-scale perturbations through diffusion damping after neutrino decoupling lowers the present-day neutrino temperature compared to the expected value of $1.96\,{\text{K}}$. This reduces the relic neutrino abundance by an amount controlled by the integral of the primordial curvature power spectrum $\Delta_{\cal R}^2(k)$. We find that a relic neutrino detection by PTOLEMY can set limits $\Delta_{\cal R}^2(k) \lesssim {\cal O}(0.1)$ on scales $k \lesssim 3 \times 10^5\,{\text{Mpc}^{-1}}$, complementary to limits from Big Bang Nucleosynthesis, spectral distortions, pulsar timing arrays, and future dark ages 21-cm observations.

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 links post-decoupling diffusion damping to a drop in relic neutrino temperature and abundance, yielding a new PTOLEMY bound on integrated small-scale power, but the sharp-cutoff assumption looks too simple.

read the letter

The core idea is that energy from damped small-scale modes after neutrino decoupling heats the photon bath instead of the neutrinos, lowering their present temperature below 1.96 K by an amount set by the integral of the curvature power spectrum. This produces a PTOLEMY constraint at the level of O(0.1) on scales up to a few times 10^5 Mpc^{-1}. That mechanism is not in the usual list of small-scale probes, so the paper does identify a fresh observable channel that could sit alongside BBN, mu-distortions, and 21-cm forecasts. The abstract states the effect and the resulting limit without hedging, which is straightforward. The full text presumably supplies the integral and the temperature-shift calculation, since the abstract alone would not justify the claim. What remains thin is the treatment of decoupling itself. Neutrino freeze-out is gradual over a temperature window of order 10 percent around 1 MeV, and the relevant modes enter the horizon near or before that epoch. Replacing an instantaneous cutoff with a proper Boltzmann evolution could shift the effective integral and weaken or strengthen the bound by a factor of a few. No error budget or numerical validation is visible in the provided material, so it is unclear how sensitive the O(0.1) number is to that modeling choice. The paper is aimed at cosmologists who already track small-scale power and neutrino observables; it is not a general review. It is worth sending to referees so they can check the decoupling calculation and any numerical implementation, even if the result ends up needing substantial revision.

Referee Report

1 major / 2 minor

Summary. The manuscript claims that diffusion damping of small-scale primordial curvature perturbations after neutrino decoupling deposits energy into the photon bath, lowering the present-day relic neutrino temperature below the standard 1.96 K value. The magnitude of this temperature shift (and thus the reduction in neutrino number density) is controlled by the integral of the primordial power spectrum Δ_R²(k). A future PTOLEMY detection of relic neutrinos could therefore set an upper limit Δ_R²(k) ≲ O(0.1) on scales k ≲ 3 × 10^5 Mpc^{-1}, providing a probe complementary to BBN, μ-distortions, PTAs, and future 21-cm observations.

Significance. If the central mechanism is robustly derived, the result would open a new observational window on the primordial power spectrum at wavenumbers inaccessible to most other probes. The proposed O(0.1) sensitivity is potentially competitive and falsifiable with upcoming PTOLEMY data, but its impact depends on whether the temperature shift can be cleanly isolated from other late-time effects.

major comments (1)

The derivation of the neutrino temperature shift (the step linking ∫ Δ_R²(k) dlnk to ΔT_ν/T_ν) assumes an instantaneous decoupling cutoff and that all dissipated energy goes exclusively into the photon bath with no back-reaction on the neutrino sector. This assumption is load-bearing for the quoted O(0.1) bound, yet neutrino decoupling is gradual (weak rates freeze out over ΔT/T ≈ 0.1) and the relevant modes k ≈ 3 × 10^5 Mpc^{-1} enter the horizon near or before decoupling; a full Boltzmann treatment could alter the effective integral and the resulting limit.

minor comments (2)

The title invokes 'acoustic reheating' but the abstract and presumably the main text do not define or distinguish this term from standard diffusion damping; a short clarifying sentence would improve readability.
No explicit integral expression, error budget, or numerical validation of the temperature shift is supplied in the abstract; including the key formula and a brief statement of the numerical method used to obtain the O(0.1) limit would strengthen the presentation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and thoughtful comments on our manuscript. The primary concern raised addresses the validity of our approximations for neutrino decoupling when linking the integrated primordial power spectrum to the relic neutrino temperature shift. We respond point by point below and have incorporated clarifications into the revised manuscript.

read point-by-point responses

Referee: The derivation of the neutrino temperature shift (the step linking ∫ Δ_R²(k) dlnk to ΔT_ν/T_ν) assumes an instantaneous decoupling cutoff and that all dissipated energy goes exclusively into the photon bath with no back-reaction on the neutrino sector. This assumption is load-bearing for the quoted O(0.1) bound, yet neutrino decoupling is gradual (weak rates freeze out over ΔT/T ≈ 0.1) and the relevant modes k ≈ 3 × 10^5 Mpc^{-1} enter the horizon near or before decoupling; a full Boltzmann treatment could alter the effective integral and the resulting limit.

Authors: We agree that neutrino decoupling is gradual, with weak interaction rates freezing out over a finite temperature interval ΔT/T ≈ 0.1 around T ≈ 1 MeV. However, the modes relevant to our bound (k ≲ 3 × 10^5 Mpc^{-1}) enter the horizon at much lower redshifts (z ≲ 10^6), well after the epoch when the bulk of neutrino decoupling has occurred. Diffusion damping and the associated energy deposition into the photon bath therefore take place in the post-decoupling regime, where neutrino-photon scattering is already suppressed. Standard treatments in the literature for similar dissipation effects (e.g., Silk damping and acoustic reheating) employ an effective instantaneous cutoff at decoupling with negligible error for the integrated energy transfer. We have added a new paragraph in Section 3.2 that explicitly discusses the timing of horizon entry relative to decoupling, provides an order-of-magnitude estimate of the correction from a gradual freeze-out (at the few-percent level), and states that this does not alter the O(0.1) sensitivity. A full numerical Boltzmann treatment would be a valuable extension but lies beyond the scope of the present work; we note this limitation and argue that it would not change the main conclusion or the quoted bound at the level of precision claimed. revision: partial

Circularity Check

0 steps flagged

No circularity: temperature shift derived as physical consequence of power-spectrum integral; PTOLEMY bound is downstream constraint

full rationale

The derivation begins from the physical process of diffusion damping of small-scale modes after neutrino decoupling, which deposits energy into the photon bath and thereby lowers the present-day neutrino temperature relative to the standard 1.96 K value. The magnitude of this shift is stated to be controlled by the integral of the primordial curvature power spectrum Δ_R²(k). This relation is presented as a calculable consequence rather than a fitted parameter or self-definition. The subsequent PTOLEMY limit Δ_R²(k) ≲ O(0.1) on k ≲ 3×10^5 Mpc^{-1} is framed as an observational consequence of that derived temperature shift, not an input that is renamed or re-fitted. No self-citations, uniqueness theorems, or ansatze are invoked in the provided text to close the chain; the central mapping remains externally falsifiable by relic-neutrino detection and independent of the paper's own fitted values. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available; the full derivation, assumptions about neutrino decoupling timing, and any numerical integrals are not provided, so the ledger is necessarily incomplete.

axioms (1)

domain assumption Standard Big Bang cosmology with neutrino decoupling occurring at a well-defined epoch after which diffusion damping can act on small-scale modes.
The claimed temperature shift presupposes the standard thermal history and decoupling redshift.

pith-pipeline@v0.9.0 · 5424 in / 1493 out tokens · 82010 ms · 2026-05-13T05:23:12.748157+00:00 · methodology

discussion (0)

Reference graph

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