A phenomenological framework for spacetime as a variable condensed medium: the speed of light as a collective velocity and its observable consequences

We develop a phenomenological framework, within the analogue-gravity and induced-gravity programmes, in which spacetime is the low-energy effective description of a coherent quantum medium (a condensate) whose density varies across the universe. Light, matter and gravity are treated as collective excitations of the medium, and the invariant speed c is identified with its sound speed. We show that, because observers are themselves built from excitations, Lorentz invariance emerges at low energy and only dimensionless combinations of constants are observable. All observable consequences are then encoded in a single dimensionless state field φ = ln(n/n₀) and three phenomenological exponents (k_α, k_μ, k_G). Using Sakharov-type induced gravity we obtain the sign of the density dependence of the gravitational coupling, G ∝ 1/n, and using the Thomas–Fermi response of the medium we obtain δn/n = −Ψ/c², which links variations of constants to the local gravitational potential. We derive the Bogoliubov dispersion relation, the sonic-horizon description of black holes with a finite core, the suppression of Hawking-spectrum modifications for astrophysical black holes, and two cosmological scenarios for the background medium, one of which predicts a logarithmic drift of the fine-structure constant at the sensitivity of forthcoming spectrographs. We confront the framework with atomic-clock, quasar-absorption, Cassini, gamma-ray-burst and GW170817 constraints, delimit the allowed parameter region, and identify one distinctive prediction: a correlation between Δα/α in absorption systems and the dark-matter density of the absorber. We state which steps are derived and which remain conjectural.