Emergent Gravitation from Vacuum Contraction

The Relativistic Contraction-Shrinking Theory (RKST) presents a fundamental reinter- pretation of the large-scale dynamics of the universe. By formulating a ghost-free scalar-tensor theory within the Horndeski class, it is shown that the gravitational constant G is not a fundamental constant of nature, but rather an emergent quantity arising from the coupling between a microscopic scale (identified with the proton radius rp) and the cosmological Dirac number N . The central result of the theory is the resolution of the cosmological constant problem through an energy partitioning in which vacuum energy is almost completely bound in the matter sector. We demonstrate that the observed accelerated expansion of the universe and the phantom equation-of-state parameter w ≈ −1.05 do not reflect an expansion of space, but rather a universal contraction of the vacuum. While preserving scale invariance and incorporating chameleon screening, the RKST reproduces both the classical solar-system tests of General Relativity and the galactic dynamics of the SPARC sample without requiring dark matter. This marks the transition from a phenomenological description to a causal ab initio field theory.