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), an effective phenomenological 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 to the density of baryonic matter. The physical foundation of this response is a dilution process: the volume of the substrate grows uniformly at every point, the energy of the medium is redistributed and equilibrated over the available geometry, and the mean energy density decreases with the expansion; within the zone of influence of an organized mass, the redistribution acts on the local gradient and extends the gravitational well to where the tension equals the renewal rate of the medium (Section 2.1). This coupling generates MOND-like dynamics at low accelerations, with the critical scale a₀ ≈ cH₀/(2π) emerging from the linear expansion Rₕ = ct as a natural scale identification. We find consistency with the Radial Acceleration Relation (RAR) through the critical screening density ρ_crit = 10⁻²² kg m⁻³ (fitted to the SPARC catalog). The “Vacuum Catastrophe” is mitigated phenomenologically through a dynamical cancellation condition, which fixes the non-minimal coupling ξ₀ ≈ −2.4×10⁻³. Finally, the kinematics of GRC suggests an extended structural collapse time at high redshift (z≈10), whose quantitative factor requires computing the emergent temporal integral τ(z). The model structurally postulates the absence of primordial B-modes (r ≈ 0) as a consequence of the lack of an inflationary period, constituting a direct observational falsification criterion. We additionally identify qualitative research directions consistent with the substrate, such as a cumulative gravitational excess in cluster lenses where the light deflection follows the same Radial Acceleration Relation as stellar dynamics, without an artificial limit on individual amplification. The total cluster excess depends on the three-dimensional distribution of galaxies and on the photon trajectory. The framework is constructed to be minimal in free parameters, with effective quantities anchored mainly to galactic phenomenology. The determination of exact magnitudes for lenses constitutes an open computational challenge, necessary for future comparisons with the CMB-S4, Euclid and LiteBIRD missions. This work does not intend to provide a complete replacement for the standard cosmological model, but to establish a minimal phenomenological framework that captures the observed scaling relations and provides testable constraints for future observations.