Admissibility-Locked Unimodular Gravity: Bianchi Slaving, Local Scalar Survival, and the Conformal Stiffness Floor

Abstract

We introduce a covariant effective framework in which the spacetime volume element is constrained by an admissibility scalar psi through a density-safe lock, sqrt(-g) = omega(x) e^psi, where omega(x) is a fixed reference scalar density inherited from coarse-graining and psi is a true scalar encoding local admissibility or routing capacity. The theory is adjacent to unimodular gravity but differs from both ordinary unimodular gravity and Henneaux–Teitelboim-type extensions: the Lagrange multiplier lambda enforcing the volume lock is not promoted to an independent propagating cosmological-constant field. Bianchi integrability instead forces lambda e^psi = Lambda*, so lambda(x) = Lambda* e^(-psi(x)); the global constant Lambda* survives as an integration constant while the local vacuum reaction is algebraically slaved to psi. The propagating degree of freedom is psi, not lambda. Because the lock identifies psi with the conformal mode of the metric, the usual wrong-sign conformal contribution from the Einstein–Hilbert action is converted into a quantitative lower bound on the psi-sector stiffness, Z_psi > 3/(8 kappa). An ADM consistency analysis shows the lapse and multiplier belong to the shared unimodular constraint sector while (psi, pi_psi) is a nondegenerate canonical pair; completion of the Dirac chain reproduces the spatial slaving condition d_i(lambda e^psi) ≈ 0, removing the local multiplier profile rather than the scalar. After separating the unimodular zero mode, the supported local field content is two tensor polarizations plus one scalar mode. The global canonical bookkeeping is left open for a Henneaux–Teitelboim completion. This paper isolates the formal covariant core of Procedural Vacuum Breakdown from its phenomenological optical-membrane bridge, which is deferred to a companion benchmark paper.

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