What question did this study set out to answer?

This study aims to elucidate how a growing neutrino mass evolves alongside dark energy, providing a distinctive observable to distinguish their effects.

June 30, 2026Open Access

Separating a Growing Neutrino Mass from Dynamical Dark Energy: the Scale-Dependent Growth Signature of an Evolving MOND Scale

Key Points

This study aims to elucidate how a growing neutrino mass evolves alongside dark energy, providing a distinctive observable to distinguish their effects.
Utilized the de Sitter-Unruh modified-inertia proposal to define the MOND acceleration scale linked to dark energy density.
Applied CAMB calculations to confirm scale-dependent changes in the matter power spectrum attributed to neutrino mass.
Leveraged Euclid Fisher analysis to assess the detectability of the predicted effects.
Found a scale-dependent suppression of structure growth below the neutrino free-streaming scale with a detectable effect of ~1.4 sigma at normal-ordering and ~3.9 sigma at Sigma=0.10 eV.
Confirmed that a growing neutrino mass creates a unique observational signature that cannot be replicated by constant dark energy models.
Estimates of the absolute neutrino mass will enhance the accuracy of the predicted scale-dependent features.

Abstract

A companion/forecast note to 'A Growing Neutrino Mass from an Evolving MOND Scale' (DOI 10. 5281/zenodo. 20977421). The de Sitter-Unruh modified-inertia proposal sets the MOND acceleration scale by the dark-energy density (a0 = cHLambda/Z = 9. 36e-11 m/s²), so a0 evolves as a0 (z) /a0 (0) = sqrt (rhoDE (z) /rhoDE (0) ). The companion note showed that IF the lightest neutrino is a swampland-tower state, its mass is locked to a0 (z) with no free amplitude, freezing by recombination so the CMB imprints a ~25-45% lighter neutrino than today's -- a right-signed reading of the DESI 'negative effective neutrino mass' anomaly. The open objection was DEGENERACY: a constant neutrino mass with GENERIC dynamical dark energy also pushes the inferred Sigma mₙu below the oscillation floor. This note identifies and quantifies the observable that breaks the degeneracy. A GROWING neutrino mass changes the free-streaming fraction fₙu (z), suppressing structure growth ONLY below the neutrino free-streaming scale kfs (z) -- a SCALE-DEPENDENT step in the matter power spectrum. Dynamical dark energy changes the expansion H (z) and is SCALE-INDEPENDENT. The scale-dependence is therefore a separator no equation-of-state mirage can reproduce (a qualitative free-streaming-vs-background fork, not a numerical coincidence). A real CAMB calculation confirms the step (~0. 65% at the normal-ordering floor, ~1. 4% at Sigma=0. 10 eV), and a focused Euclid Fisher gives a detectability of ~1. 4 sigma at the floor rising to ~3. 9 sigma at Sigma=0. 10 eV -- i. e. the test's power is HOSTAGE to the absolute neutrino mass, which JUNO (first data 2026) and KATRIN pin independently this decade. The prediction is ROBUST to the DESI DR1->DR2 update (the locked mass ratio moves by 0. 57-0. 74). HONEST SCOPE: founded-not-derived (the absolute mₙu is free; the framework forces the RATIO and the scale EdS=rhoDE^ (1/4) =2. 24 meV, not the mass) ; conditional on alpha~lambda and nu=tower; the CAMB step uses a two-constant-mass bracket and the Fisher rough single-tracer values (a publication forecast needs full Boltzmann m (z) + a multi-tracer Fisher) ; DIES if w->-1; NEUTRINO/DARK SECTOR ONLY -- NOT a theory of everything (charged-lepton and quark masses untouched and walled). Contribution: converts the companion paper's qualitative 'testable by a joint fit' into a specific, physical, dark-energy-unfakeable observable (the free-streaming step) with a computed detectability that sharpens with the absolute neutrino mass. Reproducible from the public repository.

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