A Universal Acceleration Scale Linking Galaxy Dynamics and Cosmic Expansion

This paper examines the appearance of a characteristic acceleration scale of order cH0cH_0cH0 across several independent astrophysical contexts. The quantity cH0cH_0cH0, formed from the speed of light ccc and the present-day Hubble expansion rate H0H_0H0, naturally arises in cosmology when relating the expansion rate of the universe to physical distance scales. Interestingly, an acceleration threshold of comparable magnitude is also observed empirically in galaxy rotation curves, where deviations from classical Newtonian expectations occur below a characteristic acceleration a0≈1.2×10−10 m/s2a_0 \approx 1.2 \times 10^{-10}\, \text{m/s}^2a0≈1.2×10−10m/s2. This paper explores several astrophysical quantities that can be constructed from combinations of H0H_0H0, ccc, and the gravitational constant GGG. These include the cosmic acceleration scale cH0cH_0cH0, the empirical galaxy acceleration threshold a0a_0a0, characteristic surface densities of galactic disks, and the horizon mass scale associated with the observable universe. The recurrence of similar numerical scales across these independent phenomena suggests the possibility that galaxy dynamics and cosmic expansion may be influenced by a common dynamical scale. While dimensional correspondences alone do not establish a new physical mechanism, they provide motivation for further investigation into whether these recurring scales reflect deeper structural properties of spacetime. The results presented here highlight the intriguing numerical proximity between galactic and cosmological acceleration scales and raise the possibility that phenomena typically treated separately in standard cosmology may share a common underlying origin. This work forms part of an ongoing series exploring the Relational Lens framework, in which spacetime is interpreted as a bounded dynamical domain between complementary limits associated with gravitational contraction and the propagation boundary defined by the speed of light.