What question did this study set out to answer?

This note aims to catalog a0(z) predictions and highlight a unique non-monotonic signature that differentiates it from existing models.

July 3, 2026Open Access

A Non-Monotonic a0(z) Signature: An Observational Discriminant Among Evolving-Acceleration-Scale Models in the DESI Era

Key Points

This note aims to catalog a0(z) predictions and highlight a unique non-monotonic signature that differentiates it from existing models.
Cataloged published a0(z) predictions including monotonic and flat behaviors.
Evaluated the non-monotonic behavior using DESI DR2 dynamical dark energy data.
Conducted a literature search to identify existing models and publications related to a0(z).
Identified a non-monotonic a0(z) curve peaking at z~0.4, differing from all previously cataloged models.
Demonstrated the bump in a0 ranging from +3-9% at z~0.4, followed by a decline to ~0.65-0.78 by z=3.
Established the non-monotonic curve as a falsifiable observational discriminant in the context of low and high redshift behaviors.

Abstract

A comparative-predictions note. The MOND acceleration scale a0 ~ c sqrt (Lambda) has long invited a cosmological origin and thus the possibility that a0 EVOLVES with redshift. Several couplings have been proposed and they disagree in the SHAPE of a0 (z). This note catalogs the published a0 (z) predictions and observes they are ALL monotonic or flat: RISING (a0 prop cH (z): Verlinde emergent gravity, McCulloch quantized inertia; holographic dark energy; the LambdaCDM-simulation a0 prop (1+z) ^3/4; and the MUSE-DARK III / MIGHTEE-HI rising-a0 DATA), CONSTANT (standard MOND; a0 prop sqrt (Lambda) with Lambda fixed: Blanchet-Seraille 2025; a concurrent de Sitter-Unruh modified-inertia treatment, Luo 2026, gives a STATIC a0), or monotonically DECLINING (Limbach-Psaltis-Ozel 2008 with constant w<-1). Evaluating the LPO relation a0 prop sqrt (rhoDE) instead on the DESI DR2 DYNAMICAL (w0-wa CPL) dark energy -- where rhoDE (z) is itself non-monotonic, PEAKING at the phantom crossing near z~0. 4 -- yields a qualitatively different curve: a BUMP of +3-9% in a0 at z~0. 4 followed by decline to ~0. 65-0. 78 by z=3. This non-monotonic shape is ABSENT from every rival cataloged, and a thorough (not exhaustive) literature search (4-agent sweep across the DESI x MOND intersection and the full a0 (z) landscape, deep-reads of the nearest rivals SIV/Maeder 2409. 11425 and Luo 2026 2602. 14515) found NO prior publication of it. It is therefore a clean falsifiable OBSERVATIONAL DISCRIMINANT: at low z it mimics a rising model, at high z a declining one, and only it turns over -- with the turnover pinned to the DESI-measured phantom-crossing redshift. SCOPE/CREDIT (explicit): the relation a0 prop sqrt (rhoDE) is Limbach-Psaltis-Ozel 2008 (arXiv: 0809. 2790) ; the de Sitter-Unruh modified-inertia mechanism is Milgrom 1999 (astro-ph/9805346), 1994, with concurrent Luo 2026; the rhoDE peak is standard DESI w0-wa cosmology; the high-z decline is already in LPO for w<-1; the coefficient a0=c² sqrt (Lambda/32pi) =9. 36e-11 is a one-parameter modelling CHOICE, not a derivation. The contribution is the DESI-era COMPOSITION and the identification of the non-monotonic curve as a discriminant. DETECTABILITY assessed honestly: the bump is ~0. 015-0. 037 dex in the Tully-Fisher intercept vs ~0. 05-0. 20 dex systematic floors (and ~2-3% in lensing vs a ~3-5% floor) -- BELOW current floors, a long-horizon test needing sub-2% TFR-intercept precision at 0. 3<z<0. 6. Companion to 'Scale Without Law' (10. 5281/zenodo. 21016309) and the cluster-anisotropy note (10. 5281/zenodo. 21104820). The author retracted all earlier 'theory of everything' claims (2026-06-23) ; this note makes none. Coverage caveat: 'no duplicate found', not 'none exists' -- LPO 2008's full citation tree could not be machine-enumerated (INSPIRE/Semantic-Scholar citation APIs returned broken/incomplete data for that record).

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