Geometric Response Cosmology (GRC): Induced Gravity and Emergent Time from the Energy Substrate as a Phenomenological Framework for the Dark Sector

We propose Geometric Response Cosmology (GRC), a phenomenological effective framework where time emerges as a kinematic residue of a real 3D substrate and gravity is described as an elastic response of the energy substrate through effective couplings with baryonic matter density. This coupling generates MOND-like dynamics at low accelerations, with the critical scale a0≈cH0/(2π) emerging from linear expansion Rh=ct as a natural scale identification. We find consistency with the Radial Acceleration Relation (RAR) through the critical screening density ρcrit=10−22kgm−3 (fitted to the SPARC catalog). The "Vacuum Catastrophe" is phenomenologically mitigated through a dynamic cancellation condition, which determines the non-minimal coupling ξ0≃−2.4×10−3 . Finally, GRC kinematics suggests an extended structural collapse time at high redshifts (z≈10 ), whose quantitative factor requires calculation of the emergent temporal integral τ(z) . The model identifies as its most direct observational signature the absence of primordial B-modes (r≈0 ). We additionally identify qualitative research directions consistent with the substrate, such as a cumulative gravitational excess in cluster lensing where light deflection follows the same Radial Acceleration Relation as stellar dynamics, without artificial bound on individual amplification. The total cluster excess depends on the three-dimensional galaxy distribution and the photon trajectory. The framework is constructed to be minimal in free parameters, with effective quantities primarily anchored to galactic phenomenology. The determination of exact magnitudes for lensing and BAO constitutes open computational challenges, necessary for future contrasts with CMB-S4, Euclid, and LiteBIRD missions. This work does not aim to provide a complete replacement for the standard cosmological model, but to establish a minimal phenomenological framework that captures observed scaling relations and provides testable constraints for future observations.