Non-local gravity effects in cosmological dynamics probed by IceCube/KM3NeT signals and dark matter relic abundance

Gaetano Lambiase; Giuseppe Meluccio; Salvatore Capozziello

Non-local gravity parameters can jointly explain IceCube/KM3NeT high-energy neutrino rates up to 220 PeV and the dark-matter relic abundance when the cosmic background follows Noether-derived power-law solutions.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · grok-4.5

2026-07-13 21:15 UTC pith:FATULICP

load-bearing objection Abstract-only claim that scalarised non-local cosmologies plus a portal operator jointly explain IceCube/KM3NeT PeV neutrinos and DM relic density; pipeline is uncheckable without the body. the 3 major comments →

arxiv 2603.20771 v2 pith:FATULICP submitted 2026-03-21 gr-qc astro-ph.COhep-th

Non-local gravity effects in cosmological dynamics probed by IceCube/KM3NeT signals and dark matter relic abundance

Salvatore Capozziello , Gaetano Lambiase , Giuseppe Meluccio This is my paper

classification gr-qc astro-ph.COhep-th

keywords non-local gravitycosmologyIceCubeKM3NeTdark matterhigh-energy neutrinosNoether symmetriesscalar-tensor gravity

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that non-local terms in gravity, once rewritten as ordinary scalar fields, control the expansion history of the Universe in ways that leave a clear imprint on both ultra-high-energy neutrino fluxes and the leftover dark-matter density. Using the interaction operator that couples leptons, the Higgs field and a dark fermion, the authors show that the same non-local parameters that set the cosmic expansion can simultaneously match the neutrino events reported by IceCube and KM3NeT and the observed dark-matter abundance. The background evolution is taken from exact power-law solutions that arise when Noether symmetries are present in the non-local action. A sympathetic reader would care because the result supplies a single gravitational mechanism that links two otherwise unrelated observables at the highest energies currently accessible.

Core claim

Different dynamical systems describing Universe evolution under non-local gravitational field equations are highly sensitive to the non-local gravity parameters at IceCube/KM3NeT energies. The four-dimensional operator y_αχ L̄_α H χ can therefore account for both the reported high-energy neutrino rate (up to ~220 PeV) and the dark-matter relic abundance when the cosmic background follows power-law solutions obtained from Noether symmetries of the scalarised non-local models.

What carries the argument

The operator y_αχ L̄_α H χ together with power-law cosmological solutions derived from Noether symmetries of scalarised non-local gravity actions. The operator supplies the particle-physics channel producing neutrinos and dark matter, while the Noether-derived power laws fix the expansion history that sets the production rates.

Load-bearing premise

That non-local curvature and torsion terms can be rewritten as ordinary scalar fields without changing the cosmological solutions relevant at IceCube/KM3NeT energies, and that the power-law solutions coming from Noether symmetries accurately describe that background.

What would settle it

A joint fit of the operator and the Noether power-law backgrounds to IceCube/KM3NeT neutrino event rates and the observed dark-matter density fails for every value of the non-local parameters that remains consistent with other cosmological constraints.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

The measured neutrino spectrum above PeV energies can directly constrain the free parameters of non-local gravity.
Successful joint fits would favour non-local models that admit Noether symmetries over those that do not.
Future higher-energy neutrino events would further discriminate among different scalarised non-local cosmologies.
The same framework predicts a correlated dark-matter abundance that can be checked against independent cosmological probes.

Where Pith is reading between the lines

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

If the joint explanation holds, non-local gravity becomes a concrete bridge between quantum-gravity-inspired corrections and multi-messenger astronomy.
The same scalarisation procedure could be tested with other high-energy astrophysical messengers such as ultra-high-energy cosmic rays.
Once cosmological parameters are fixed, laboratory or collider searches for the dark fermion χ could independently bound the coupling y_αχ.
Power-law Noether solutions may serve as a practical template for reconstructing non-local actions from multi-messenger data.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

Abstract-only claim that scalarised non-local cosmologies plus a portal operator jointly explain IceCube/KM3NeT PeV neutrinos and DM relic density; pipeline is uncheckable without the body.

read the letter

The one thing you need to know is that this is an abstract-only piece: Capozziello, Lambiase and Meluccio argue that scalarised non-local (curvature/torsion) cosmologies, reduced to scalar-tensor form and restricted to Noether power-law backgrounds, make the expansion history sensitive enough at IceCube/KM3NeT energies that the portal y_{αχ} L̄_α H χ can simultaneously match the reported PeV neutrino rate (up to ~220 PeV) and the dark-matter relic abundance. That joint application is the actual novelty claim; the ingredients themselves (non-local scalarisation, Noether cosmologies, freeze-in portals) are already in the literature.

What the abstract does cleanly is state the program without overselling a new theory of gravity. It is explicit about the reduction to scalar-tensor gravity and about using Noether-derived power laws rather than inventing a new expansion history. If the full paper actually derives the field equations, exhibits the Noether generators, writes down a(t) ~ t^p, and shows a Boltzmann or freeze-in calculation with the portal, that would be a legitimate multi-messenger handle on non-local parameters. Self-citation of prior Noether work is not a flaw if those symmetries are used correctly.

The soft spots are exactly the ones the stress-test flags, and they are epistemic rather than demonstrated contradictions. We cannot audit whether scalarisation preserves the solutions that matter at PeV scales, whether the power-law backgrounds are the relevant ones for both the neutrino rate and the relic density, or how many free non-local parameters plus y_{αχ} are dialed to fit. Soundness and circularity scores have to stay provisional; there are no equations, no sensitivity plots, no baselines. That is not a load-bearing flaw we can prove from the abstract—it is simply missing intermediate results.

This is for people already working on non-local or scalar-tensor cosmologies who also care about multi-messenger constraints. A serious referee should see the full manuscript if the journal’s scope includes that intersection; the claim is important enough within the subfield to deserve a proper look rather than a desk reject on the abstract alone. I would not bring the abstract to reading group, and I would not cite it yet. Once the body is available, the decision becomes whether the pipeline is actually closed or just sketched.

Referee Report

3 major / 3 minor

Summary. The manuscript claims that curvature- and torsion-based non-local gravity models can be scalarised and reduced to scalar-tensor form, yielding cosmological dynamical systems that are highly sensitive to non-local parameters at IceCube/KM3NeT energies (neutrino fluxes up to ~220 PeV). Adopting power-law backgrounds inferred from Noether symmetries of those models, and the portal operator y_{αχ} L̄_α H χ, the authors argue that both the reported high-energy neutrino rate and the dark-matter relic abundance can be jointly explained.

Significance. If the full derivations and quantitative results hold, the work would link non-local modified gravity to multi-messenger data (IceCube/KM3NeT) and dark-matter cosmology in a single portal framework, potentially constraining non-local parameters with PeV-scale observations. Use of Noether-symmetry power-law solutions, if machine-checked or fully explicit, would be a methodological asset. With only the abstract available, however, none of these strengths can be verified, so the significance remains conditional on material not provided for review.

major comments (3)

The abstract’s central claim that ‘different dynamical systems … can be highly sensitive to the parameters of non-local gravity at energies probed by IceCube/KM3NeT’ is unsupported in the available text: no field equations, no numerical values of non-local parameters, no sensitivity plots, and no quantitative comparison to the ~220 PeV rate are given. This sensitivity is load-bearing for the paper’s thesis and cannot be assessed from the abstract alone.
The joint explanation of the neutrino rate and DM relic abundance via y_{αχ} L̄_α H χ presupposes Noether power-law backgrounds. The abstract states that such solutions are ‘inferred by the existence of Noether symmetries’ but supplies neither the Noether generators, the resulting a(t)∼t^p forms, nor the Boltzmann/freeze-out calculation that would establish a simultaneous fit. Without those intermediate results the joint-explanation claim is not checkable.
The reduction of non-local curvature- and torsion-based terms by ‘scalarisation’ to scalar-tensor gravity is asserted as valid for the cosmological backgrounds used at PeV energies. The abstract gives no demonstration that the scalarised solutions remain applicable at IceCube/KM3NeT scales, nor any statement of the domain of validity of the reduction. This step is essential to the claimed applicability of the framework.

minor comments (3)

The term ‘scalarised’ appears in quotation marks without a one-line definition; even an abstract-level clarification of the procedure would aid readability.
The portal is written y_{αχ} L̄_α H χ; the nature of χ (DM candidate?), the index conventions, and whether the operator is four-dimensional in the spacetime or interaction sense should be stated more clearly.
‘Four-dimensional operator’ is slightly ambiguous; tightening the wording would avoid confusion with four-fermion contact terms.

Circularity Check

0 steps flagged

Abstract-only review: no verifiable circularity; no equations, fits, or self-citation chains available to exhibit any reduction by construction.

full rationale

Only the abstract is available. It states that non-local terms are scalarised to scalar-tensor gravity, that power-law solutions from Noether symmetries are adopted as the background, and that the portal operator y_{αχ} L̄_α H χ is used to address both the IceCube/KM3NeT neutrino rate and the DM relic abundance, with claimed sensitivity of the dynamical systems to non-local parameters. Per the hard rules, circularity may be claimed only when a specific reduction can be quoted and exhibited (e.g., a fitted parameter re-labeled as a prediction, or a load-bearing uniqueness claim that reduces to an unverified self-citation). No field equations, Noether generators, scale-factor solutions, Boltzmann calculations, numerical scans, or citations appear in the supplied text, so none of the six enumerated patterns can be demonstrated. The honest finding is therefore no significant circularity (score 0); any concern about parameter tuning or the scalarisation/Noether pipeline remains an epistemic gap outside the circularity criterion.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 0 invented entities

Abstract-only: free parameters and axioms are those named or implied by the abstract’s mechanism. Non-local gravity parameters and the portal coupling are the main adjustable quantities; scalarisation and Noether power-law solutions are load-bearing domain assumptions. No new particle species beyond a standard portal χ is clearly invented; non-local gravity itself is prior framework, not a new entity invented here.

free parameters (2)

non-local gravity parameters (unspecified)
Abstract states dynamical systems are highly sensitive to non-local gravity parameters at IceCube/KM3NeT energies; values are not given and must be chosen or fitted to match observables.
portal coupling y_{αχ}
Four-dimensional operator y_{αχ} L̄_α H χ is introduced to explain both neutrino rate and DM abundance; the Yukawa-like strength is a free parameter of the particle sector.

axioms (3)

domain assumption Non-local curvature- and torsion-based terms can be scalarised and reduced to scalar-tensor gravity without losing the cosmological effects claimed.
Stated as the modeling framework in the abstract; not derived here.
domain assumption Power-law cosmological solutions inferred from Noether symmetries adequately describe the background at energies relevant to IceCube/KM3NeT and DM freeze-in/relic calculation.
Abstract adopts these solutions as the dynamical background; validity at PeV-scale phenomenology is assumed.
ad hoc to paper The operator y_{αχ} L̄_α H χ is the relevant interaction linking neutrino flux and DM relic abundance in this setup.
Chosen specifically to address both observables; alternative portals are not compared in the abstract.

pith-pipeline@v1.1.0-grok45 · 6107 in / 2813 out tokens · 36334 ms · 2026-07-13T21:15:00.958401+00:00 · methodology

0 comments

read the original abstract

Non-local gravity terms have a relevant role in determining the cosmological dynamics. Here we consider curvature- and torsion-based cosmological models where non-local terms can be ``scalarised'' and then reduced under the standard of scalar-tensor gravity. In this context, we study the role of non-local cosmology with regards to the recent results reported by the IceCube/KM3NeT experiments, which revealed high-energy astrophysical neutrino fluxes up to energies of $220$\,PeV. Specifically, we consider the four-dimensional operator $y_{\alpha\chi}\bar L_\alpha H\chi$ in order to explain both the neutrino rate result and the abundance of dark matter in the Universe, provided that the cosmological background evolves according to non-local gravitational field equations. We show that different dynamical systems representing the evolution of the Universe can be highly sensitive to the parameters of non-local gravity at energies probed by IceCube/KM3NeT. In particular, we adopt power law solutions inferred by the existence of Noether symmetries in non-local cosmological models.

Non-local gravity effects in cosmological dynamics probed by IceCube/KM3NeT signals and dark matter relic abundance

Core claim

What carries the argument

Load-bearing premise

What would settle it

If this is right

Where Pith is reading between the lines

discussion (0)