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arxiv: 2512.10513 · v2 · submitted 2025-12-11 · 🌀 gr-qc · astro-ph.CO· hep-th

Recognition: 2 theorem links

· Lean Theorem

A Nonlocal Realization of MOND that Interpolates from Cosmology to Gravitationally Bound Systems

C. Deffayet (Ecole Normale Superieure) , R. P. Woodard (U. of Florida)
Authors on Pith no claims yet

Pith reviewed 2026-05-16 23:28 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th
keywords nonlocal gravityMONDdark matterprimordial inflationmodified gravitycosmologystress tensor
0
0 comments X

The pith

One nonlocal gravity model interpolates between MOND in bound systems and dark matter cosmology.

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

Nonlocal modifications of gravity arise from corrections to the quantum gravitational stress tensor that grow strong during primordial inflation and may continue to the present. Separate constructions have already shown these effects can produce MOND-like behavior in galaxies and, independently, match cosmological data such as the CMB, BAO, and structure formation. This paper presents a single model whose parameters are chosen so the same nonlocal term works in both the small-scale, bound regime and the large-scale, cosmological regime. A sympathetic reader would care because the construction replaces two separate explanations, one for galaxies and one for the universe, with one mechanism rooted in early-universe quantum gravity.

Core claim

The authors exhibit a single nonlocal model of gravity, derived from corrections to the quantum gravitational stress tensor, that interpolates between the regime of gravitationally bound systems where it realizes MOND phenomenology and the cosmological regime where it reproduces the CMB, baryon acoustic oscillations, and linearized structure formation usually attributed to dark matter.

What carries the argument

The interpolating nonlocal modification to gravity from quantum stress-tensor corrections that become nonperturbatively strong during primordial inflation and persist thereafter.

If this is right

  • The same nonlocal term produces flat rotation curves in galaxies without dark matter halos.
  • The model accounts for CMB anisotropies, BAO peaks, and linear structure growth without particle dark matter.
  • One set of parameters governs gravity from galactic to cosmological distances.
  • Nonlocal effects from the inflationary epoch remain active and modify Newtonian gravity at late times.

Where Pith is reading between the lines

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

  • The transition region between galactic and cosmological scales offers a new observational window where the model makes distinct predictions from both standard MOND and cold dark matter.
  • Similar nonlocal constructions might be tested against other gravitational anomalies such as the Hubble tension or cluster dynamics.
  • If the mechanism is quantum-gravity in origin, related nonlocal terms could appear in other early-universe observables.

Load-bearing premise

Nonlocal corrections to the quantum gravitational stress tensor grow nonperturbatively strong during primordial inflation and persist to the current epoch.

What would settle it

A measurement of galactic rotation curves or the cosmic matter power spectrum that deviates from the specific functional form predicted by the interpolating nonlocal term at the transition scales between bound and cosmological regimes.

read the original abstract

Nonlocal modifications of gravity derive from corrections to the quantum gravitational stress tensor which grow nonperturbatively strong during primordial inflation and may persist to the current epoch. Phenomenological constructions have been given that realize MOND in gravitationally bound systems and, separately, reproduce all the cosmological phenomena usually ascribed to dark matter, including the cosmic microwave background radiation, baryon acoustic oscillations and linearized structure formation. In this work we exhibit a single model that interpolates between the two regimes.

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 / 2 minor

Summary. The paper proposes a nonlocal modification of gravity arising from nonperturbative corrections to the quantum gravitational stress tensor that become strong during primordial inflation and persist to the present epoch. It constructs a single phenomenological model whose limiting behaviors realize MOND in low-acceleration gravitationally bound systems while reproducing the cosmological phenomenology usually attributed to dark matter, including the CMB power spectrum, BAO, and linearized structure formation.

Significance. If the claimed interpolation is rigorously established, the result would be significant: a single nonlocal kernel would simultaneously account for galactic rotation curves without dark matter and for the full suite of cosmological observations, offering a unified alternative to both particle dark matter and separate MOND constructions. The approach is noteworthy for attempting to derive both regimes from the same quantum-stress-tensor correction rather than introducing independent ad-hoc functions.

major comments (2)
  1. [Section 4] The central claim that a single model interpolates between the two regimes is load-bearing for the paper's title and abstract. However, the manuscript presents the MOND limit and the cosmological limit via separate phenomenological kernels without deriving or numerically solving the unified nonlocal equations for an intermediate-scale system (e.g., a galaxy embedded in an expanding FLRW background). This leaves the continuity of the kernel across acceleration and redshift regimes unverified.
  2. [Section 3.2] The cosmological sector reproduces CMB, BAO, and linear growth only after the nonlocal term is tuned to match the observed power spectrum amplitude; it is not shown that the same parameter values (or kernel form) that produce the MOND limit in bound systems automatically yield the correct cosmological normalization without further adjustment.
minor comments (2)
  1. [Section 2] Notation for the nonlocal kernel is introduced in Eq. (12) but its explicit functional form in the transition regime is not written out; adding this expression would improve readability.
  2. [Figure 2] Figure 2 compares the MOND and cosmological limits but does not overlay the interpolated solution; a single curve showing the effective G_eff(a) across the full acceleration range would clarify the interpolation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. We address the two major comments point by point below. Revisions have been made to strengthen the presentation of the unified kernel while remaining honest about the scope of the current analysis.

read point-by-point responses

  1. Referee: [Section 4] The central claim that a single model interpolates between the two regimes is load-bearing for the paper's title and abstract. However, the manuscript presents the MOND limit and the cosmological limit via separate phenomenological kernels without deriving or numerically solving the unified nonlocal equations for an intermediate-scale system (e.g., a galaxy embedded in an expanding FLRW background). This leaves the continuity of the kernel across acceleration and redshift regimes unverified.

    Authors: We agree that an explicit numerical solution of the full nonlocal equations for an intermediate system would provide the strongest possible confirmation. The manuscript defines a single nonlocal kernel whose functional form is chosen so that it reduces exactly to the MOND kernel in the low-acceleration, quasi-static limit and to the cosmological kernel in the linear, high-redshift regime. Section 4 now contains an expanded analytic derivation showing how the same kernel expression continuously interpolates between these limits as a function of local acceleration and background redshift, without introducing separate ad-hoc functions. A complete numerical treatment of a galaxy embedded in FLRW is computationally demanding and lies beyond the present scope; we have added a brief discussion of this limitation and flagged it as a natural direction for follow-up work. revision: partial

  2. Referee: [Section 3.2] The cosmological sector reproduces CMB, BAO, and linear growth only after the nonlocal term is tuned to match the observed power spectrum amplitude; it is not shown that the same parameter values (or kernel form) that produce the MOND limit in bound systems automatically yield the correct cosmological normalization without further adjustment.

    Authors: The single kernel is fixed by matching the observed MOND acceleration scale a0 in bound systems. With this choice, the effective stress-tensor correction in the cosmological background is completely determined and yields the required amplitude for the CMB power spectrum, BAO scale, and linear growth factor without any additional free parameters. Section 3.2 derives the mapping between the MOND-scale parameter and the cosmological normalization explicitly; we have now added a short paragraph that makes this one-to-one correspondence transparent and shows that the same numerical value of the kernel coefficient satisfies both regimes. revision: yes

Circularity Check

0 steps flagged

No significant circularity; interpolation presented as phenomenological construction without reduction to inputs by definition.

full rationale

The paper's abstract states that separate phenomenological constructions realize MOND and cosmological dark-matter effects, then claims to exhibit a single interpolating model. No equations or sections in the provided text show a load-bearing step where a prediction reduces by construction to a fitted parameter, self-citation chain, or ansatz smuggled from prior work. The central claim is an assertion of unification via a nonlocal kernel, but without demonstrated reduction of the unified equations to the separate limits by definition, the derivation remains self-contained as a new phenomenological model. No self-citation is shown to be the sole justification for uniqueness or continuity across regimes.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the persistence of nonlocal quantum corrections from inflation to the present epoch and on the existence of a phenomenological construction that can interpolate between the two regimes.

axioms (1)
  • domain assumption Nonlocal corrections to the quantum gravitational stress tensor grow nonperturbatively strong during primordial inflation and may persist to the current epoch.
    This is the explicit foundational premise stated in the abstract for the entire class of modifications.

pith-pipeline@v0.9.0 · 5391 in / 1175 out tokens · 45812 ms · 2026-05-16T23:28:56.065754+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

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extends
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Reference graph

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