Gravitation as an Emergent Covariant Relaxation: Variational Formalism, Bimetric Cosmological Equilibrium, and Observational Constraints

We present a rigorous bimetric variational formulation of emergent gravitation driven by the universal equilibrium-seeking principle. The spatial imbalance field is formally defined via a coordinate-invariant scalar projection mapping the physical metric onto a non-dynamic, maximally symmetric reference background. Utilizing the Palatini variational framework, we derive the exact field equations without phenomenological assumptions, demonstrating how the Einstein field equations emerge asymptotically during localized dynamic stabilization. Crucially, the model is contrasted with existing thermodynamic and entropic gravity paradigms. To test the falsifiability of the framework, we constrain the parameterized dark energy equation of state using current observational bounds from Planck, DESI, and Pantheon+, establishing a strict physical limit on the cosmic relaxation coefficient.

Hali tarjima qilinmagan