What does this research mean for the field?

A khronon-split bimetric theory successfully embeds MOND phenomenology with a dark-energy-anchored acceleration scale, passing multiple mathematical consistency tests including the absence of the Boulware-Deser ghost, and predicts a static baryonic Tully-Fisher normalization up to z~20. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

Construct and evaluate a consistent bimetric completion of modified Newtonian dynamics (MOND) where the acceleration scale $a_0$ is derived directly from dark sector pressure via a dynamical khronon field.

August 23, 2026Open Access

A Khronon-Split Bimetric Host for the Dark-Energy-Anchored Acceleration Scale: Construction, Constraint Structure, and the Ghost Test

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Authors

CZCarl P. ZimmermanAd-Tech (United States)

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Implication

Theoretical analysis uncovers a ghost-free bimetric framework for modified Newtonian dynamics using a dynamical khronon field, indicating that dark energy pressure anchors modified galactic...

Key Points

Construct and evaluate a consistent bimetric completion of modified Newtonian dynamics (MOND) where the acceleration scale $a_0$ is derived directly from dark sector pressure via a dynamical khronon field.
Coupled two Einstein-Hilbert sectors with a shift-symmetric Dirac-Born-Infeld khronon field supplying dark energy ($w = -1$) and dark abundance as a conserved charge.
Formulated the interaction via a khronon-projected connection difference and performed Arnowitt-Deser-Misner (ADM) and Dirac constraint analyses to assess the lapse Hessian and degrees of freedom.
Tested constraint brackets and ghost propagation on an explicit discretized lattice representative evaluated against pure General Relativity control baselines.
Demonstrated that the projected connection difference is lapse-free with a vanishing lapse Hessian, confirming seven physical degrees of freedom ($2+5$) and ruling out the Boulware-Deser ghost mode via non-zero on-shell constraint brackets.
Derived the interaction slope in closed form without negative coupling by hand ($M^2 = 1/8\pi G$), automatically yielding Newtonian solar system screening while strengthening galactic gravity.
Predicted an essentially static baryonic Tully-Fisher relation across redshifts $0 < z < 20$ (velocity shifts between $10^{-9}$ and $10^{-6}$ at $z = 1\text{--}5$) followed by a sharp drop at $z \approx 26$ ($1\%$) and $z \approx 48$ ($10\%$).

Cite This Study

Carl P. Zimmerman (2026) studied this question.

synapsesocial.com/papers/6a8aade47677a34114446756 https://doi.org/10.5281/zenodo.22033860

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Implication

Theoretical analysis uncovers a ghost-free bimetric framework for modified Newtonian dynamics using a dynamical khronon field, indicating that dark energy pressure anchors modified galactic...

A Khronon-Split Bimetric Host for the Dark-Energy-Anchored Acceleration Scale: Construction, Constraint Structure, and the Ghost Test

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Key Points

Cite This Study

A Khronon-Split Bimetric Host for the Dark-Energy-Anchored Acceleration Scale: Construction, Constraint Structure, and the Ghost Test

Discussion

Member takes

Implication

Key Points

Cite This Study

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