Unified Variational Gravity with Dynamical Stabilization of Energy–Momentum Conservation: Cosmology, Quantum Gravity Interpretation, and Observational Constraints

Abstract We present a unified variational framework in which deviations from covariant energy–momentum conservation are dynamically suppressed via a quadratic constraint functional appended to the Einstein–Hilbert action. We carefully define the constraint scalar, perform the variational derivation explicitly, and obtain the corrected field equations including the full form of Δ_μν (λ). The theory is reduced to the FLRW cosmological setting with the modified Friedmann and fluid equations derived from first principles. We establish a Lyapunov-style stability argument, connect the coupling λ to observational bounds from gravitational-wave speed measurements (LIGO/Virgo), CMB power-spectrum constraints, and black-hole ringdown spectroscopy, all stated in consistent physical units. Connections to holographic entropy, tensor network interpretations of spacetime, and AdS/CFT correspondence are developed as formal consequences of the framework rather than decorative context. Throughout, the framework is interpreted within the Universal Balance-Feedback Framework (UBFF), in which conservation laws represent dynamical equilibria governed by feedback attractor mechanisms. The theory reduces exactly to General Relativity in the limit λ → 0.