Rotation Curves Without Dark Matter Particles

The Dark Matter Problem

Galaxy rotation curves have been the primary evidence for dark matter since Rubin and Ford's observations in the 1970s. Stars in the outer regions of galaxies orbit too fast for the visible mass to hold them gravitationally. The standard explanation posits a halo of invisible “dark matter” particles surrounding each galaxy.

Despite decades of searches, no dark matter particle has been directly detected. Meanwhile, the empirical MOND relation (Milgrom 1983) accurately predicts rotation curves across galaxy types with a single parameter a₀.

The STF Mechanism

The STF provides a physical mechanism for MOND-like behavior. When local gravitational acceleration drops below a₀ = cH₀/(2π), the scalar field activates and modifies the effective gravitational force. This is not an ad hoc modification but a natural consequence of the field's coupling to curvature rate:

• In strong-field regions (a >> a₀): scalar field is dormant, gravity is standard GR
• In weak-field regions (a < a₀): scalar field activates, effective gravity transitions to MOND-like scaling
• The transition is smooth and controlled by the field equation

Predictions Beyond MOND

While matching MOND's empirical success, the STF makes additional predictions that differ from both ΛCDM and classical MOND:

• The acceleration scale a₀ varies with redshift as H(z)
• Cluster-scale dynamics show a specific departure pattern from MOND
• The transition radius r_t = √(GM/a₀) matches where rotation curves flatten