Interposing a Varying Gravitational Constant Between Modified Newtonian Dynamics and Weak Weyl Gravity

Area of Science:

• Astrophysics
• Cosmology
• Theoretical Physics

Background:

• The Newtonian gravitational constant G is dimensionally linked to mass, acceleration, and speed.
• Empirical baryonic Tully-Fisher (BTF) and Faber-Jackson (BFJ) relations imply G*a = constant.
• Newtonian dynamics cannot explain the origin of BTF and BFJ relations.

Purpose of the Study:

• To resolve the empirical cutoff acceleration (a0) in modified Newtonian dynamics (MOND).
• To propose a physical explanation for the observed BTF and BFJ relations.
• To introduce a variable gravitational constant G(a) dependent on acceleration.

Main Methods:

• Dimensional analysis of the gravitational constant G.
• Reinterpreting MOND by proposing G is inversely proportional to acceleration (G ∝ a⁻¹).
• Connecting high-acceleration phenomena to conformal Weyl gravity.

Main Results:

• A variable G(a) naturally explains BTF and BFJ relations without an empirical cutoff.
• Lower accelerations lead to a boosted gravitational force due to increased G.
• This framework allows quantitative mapping of G variations across cosmic scales.

Conclusions:

• The proposed G ∝ a⁻¹ relationship offers a physical resolution to MOND's limitations.
• This variable gravity model provides a unified explanation for galaxy dynamics and fundamental constants.
• The findings link galactic dynamics to the weak-field limit of conformal Weyl gravity.