A relativistic scalar-tensor theory with a fixed scale a₀: linking galaxy dynamics and cosmology

Abstract / Description This paper presents a novel relativistic scalar-tensor theory of gravity, in which the coupling constant between matter and the scalar field is fixed by a fundamental acceleration scale a₀, i.e., β = sqrt(a₀)/c. The theory aims to provide a self-consistent foundation for the empirical Radial Acceleration Relation (RAR) observed at galactic scales, accounting for its phenomenological success without the need for particle dark matter. In the weak-field limit, the theory naturally recovers MOND-like behavior. Through a chameleon-type screening mechanism, it automatically reverts to General Relativity in high-curvature environments such as the Solar System, thereby satisfying stringent local tests of gravity. Furthermore, the scalar field, endowed with an exponential potential, can drive the late-time cosmic acceleration, offering a potential framework to bridge galactic-scale dynamics with cosmology. We briefly explore the model’s potential in alleviating the Hubble tension via modifications to the pre-recombination sound horizon. The work outlines the theoretical construction, its implications for galactic dynamics and cosmology, and discusses testable predictions, including distinctive signatures in gravitational lensing, structure formation, and possible additional polarizations in gravitational waves.