Constraint–Density Scalar–Tensor Gravity

Constraint–Density Scalar–Tensor Gravity presents a minimal scalar–tensor extension of General Relativity in which spacetime curvature is sourced not only by the matter stress–energy tensor, but also by a covariant scalar field χ interpreted as a constraint–density variable. The theory is formulated within standard covariant field theory using a Jordan-frame action in which the Ricci scalar is nonminimally coupled to a scalar-dependent function F(χ). The action includes a canonical kinetic term with positive-definite coefficient Z(χ) and a scalar potential V(χ). The nonminimal coupling allows spacetime curvature to respond to spatial and temporal variations in the constraint–density field, while the scalar potential enforces a finite viability window, χ_min ≤ χ ≤ χ_max. This ensures internal consistency and recoverability of General Relativity in appropriate limits. Field equations are derived from an action principle, and conditions for stability, ghost avoidance, and classical consistency are discussed. No teleological, observer-dependent, or metaphysical assumptions are introduced. The scalar field χ is treated strictly as a phenomenological covariant degree of freedom; no claim is made regarding its fundamental or ontological status. All equations and derivations are provided in the associated PDF.