A Khronon-Split Bimetric Host for the Dark-Energy-Anchored Acceleration Scale: Construction, Constraint Structure, and the Ghost Test
Year: 2026
Type: preprint
Abstract: A bimetric completion of MOND phenomenology carrying the acceleration-scale identity a0^2 = kappa^2 G(-K(Q)) -- the MOND scale as the dark sector's pressure -- pushed through every consistency gate the programme's published filter can pose. Every gate faced, passed; closure NOT claimed, and the two remaining items are named, one adverse-leaning. THE CONSTRUCTION: two Einstein-Hilbert sectors; a shift-symmetric khronon whose beta=1 DBI kernel supplies dark energy (w = -1 exactly), a cold dust component carrying the full dark abundance as a conserved charge, and a DERIVED a0(z); and an interaction built from the khronon-projected connection difference, entering as V = sqrt(h)[N F(X) + Nhat B(X)]. The foliation is a dynamical field, not a gauge choice; full diffeomorphism invariance is kept. SIX RESULTS, each with a committed self-checking script: (1) after the Hassan-Rosen-type shift redefinition, the projected connection C_M = (Gamma3 - Gamma3hat) - Khat u is EXACTLY lapse-free, and the interaction's lapse Hessian vanishes identically -- all four entries, not a diagonal zero. (2) The quasi-static reduction of a bimetric theory is a two-potential Moebius map, not AQUAL; inverting it for the a0-line g_obs^2 = g_bar^2 + a0 g_bar gives the interaction slope in CLOSED FORM, alphahat F' = (1-R)/(R(1+r)-1) with R = (sqrt(1+4x^2)+1)/2x -- single-valued and monotone, so the legality condition that excludes this same phenomenology in AeST is satisfied here. Free content: one function fixed by the a0-line plus ONE number r = M_f^2/M_g^2. The interaction switches itself off in the Newtonian limit: solar-system screening from the required force law, not a kernel choice. (3) The sign that makes gravity stronger is DERIVED: calibrating the EH quadratic coefficient against the Newtonian limit (M^2 = 1/8piG recovered exactly) forces the MIXED contraction C^i_jk C^j_ik = -|grad psi|^2. No negative coupling by hand. (4) Both lapses appear linearly; the relative shift is determined algebraically; the degree-of-freedom count is 7 = 2 + 5, the ghost-free bimetric number, conditional on one bracket. (5) THE GHOST TEST: {F(X), B(X)} = 0 identically (two functions of the same phase-space scalar), collapsing {C, Chat} to two cross terms; on an explicit lattice representative with EVERY constraint imposed at EVERY site and both controls passing exactly, the on-shell bracket is NONZERO at a generic real point. First-classness is universal, so the ghost-propagating alternative is REFUTED on the representative: the pair is second class and the Boulware-Deser mode is removed there. (6) The exact ADM kinetic reduction is then derived (exact Legendre transform, round-trip verified, exact sqrt(h)R3), and THE VERDICT SURVIVES IT UNCHANGED. V2 adds result (7), the artifact verification: the representative's full-rank multiplier matrix (naively, frozen lapses) is dispatched by its own control -- PURE GR, first class in the continuum, FAILS THE IDENTICAL TEST on the identical lattice (on-shell brackets of rank 2 at magnitudes within 4x of the interacting theory's), and both obstructions move under a boundary-stencil change alone. The frozen-lapse finding is therefore a LATTICE ARTIFACT, uninformative rather than adverse. The ghost verdict is untouched: it rests on the bracket being NONZERO, and that direction's control (interaction off => bracket exactly zero) passed artifact-free on the same lattice. NOT CLAIMED: closure. Remaining, one theorem-grade item: the continuum Dirac analysis. Also remaining on the physics fronts: a Boltzmann run, lensing Phi+Psi, clusters, and the dust-binding question. OBSERVATIONAL SHAPE: the derived a0(z) predicts an essentially STATIC baryonic Tully-Fisher normalisation across 0 < z < 20 (velocity shifts 1e-9 to 1e-6 at z = 1-5), then a cliff (1% at z ~ 26, 10% at z ~ 48) -- a shape no constant-a0 or smoothly-evolving-a0 model has, and two-sided: any robust per-cent-level detection of a0 evolution below z ~ 5 would need nu0 three to four orders of magnitude above its independent ceilings and falsifies the law outright. kappa = 1/2 is FITTED (0.529 +/- 0.034), never derived; both a0 footings (9.3619e-11 canonical, 1.1279e-10 alt) are carried throughout; the a0-Lambda COINCIDENCE is prior art (Milgrom 1999; Blanchet & Le Tiec 2009; Pikhitsa 2010; Klinkhamer & Kopp 2011) and the IDENTITY is this programme's contribution. There is no dark-matter PARTICLE here; the dark abundance is a field's conserved charge, present in full. Six errors made during this programme -- roughly half manufactured deficits, half manufactured wins -- are recorded, dated, with directions stated, in the repository's RETRACTIONS.md, together with the standing rules extracted from them. Underlying theories: Milgrom's BIMOND/QUMOND and the Hassan-Rosen constraint mechanism; previous host analysis: Skordis-Zlosnik's AeST.
Author: Zimmerman, Carl P.
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203901884