Dynamical constants in cosmology: an invariant c-G coupling

We explore a cosmological scenario in which the speed of light c and the gravitational constant G evolve with the scale factor a in a correlated manner such that the combination c(a)⁴/G(a) remains constant. We show that this condition preserves the fundamental coupling between geometry and energy in Einstein’s equations, allowing the global evolution of the scale factor to be formally close to that of the ΛCDM model, albeit based on an alternative underlying physics in which the cosmological constant emerges as a dynamic equilibrium state rather than as an ad hoc fundamental parameter.However, the scenario exhibits physically significant differences in early causality, horizon structure, and cosmological scales.The paper is completed with five appendices dedicated to exploring the possible physical implications of the proposed scenario in various cosmological contexts, including the stability of atomic properties via the fine-structure constant, a possible resolution of the Hubble tension through sound-horizon recalibration, a new interpretation of dark energy as a product of relaxation toward an attractor, the early genesis of supermassive black holes observed by JWST, and several observational signatures of the model in the cosmic microwave background, primordial gravitational waves, and the formation of the first cosmic structures.