Flat Galactic Rotation Curves Interpreted as Evidence for the Mach's Principle

The paper explores a Machian interpretation for asymptotically flat rotation curves in disk galaxies, offering an alternative to both the ΛCDM paradigm and MOND. The authors argue that MOND's acceleration scale a₀ is not a fundamental constant but a manifestation of cosmic scales, with a₀ ~ c²/Rᵤ ~ c⁴/GMᵤ ~ c/tᵤ where Rᵤ, Mᵤ, and tᵤ are the radius, mass, and age of the observable Universe.

As a key step, they rewrite the Baryonic Tully-Fisher Relation in cosmological form: M_bar/M_u = (V/c)⁴, where V is the flat rotation velocity. This suggests that the transition to the non-Newtonian regime occurs when local accelerations become small enough to feel the global cosmic boundary, and that any Machian interpretation must satisfy this relation. The framework also predicts a cosmological evolution of the BTFR normalization as the observable Universe's mass grows.

Testing these predictions against high-redshift observations at z ~ 2 and z ~ 5, the authors find that the data favor a flat, baryon-only, Λ-dominated quasi-de Sitter universe (Ω_m ≈ 0.05, Ω_Λ ≈ 0.95) over standard MOND or ΛCDM parameters. They conclude that flat galactic rotation curves may be compelling evidence for Mach's Principle, at least in some of its versions.