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

Abstract

The Newtonian gravitational constant $G$ obeys the dimensional relation $[G][M][a]=[v{]}^4$, where $M$, $a$, and $v$ denote mass, acceleration, and speed, respectively. Since the baryonic Tully-Fisher (BTF) and Faber-Jackson (BFJ) relations are observed facts, this relation implies that $Ga=\mathrm{constant}$. This result cannot be obtained in Newtonian dynamics which cannot explain the origin of the BTF and BFJ relations. An alternative, modified Newtonian dynamics (MOND) assumes that $G=G_0$ is constant in space and derives naturally a characteristic constant acceleration $a=a_0$, as well as the BTF and BFJ relations. This is overkill and it comes with a penalty: MOND cannot explain the origin of $a_0$. A solid physical resolution of this issue is that $G\propto a^{-1}$, which implies that in lower-acceleration environments the gravitational force is boosted relative to its Newtonian value because $G$ increases. This eliminates all problems related to MOND's empirical cutoff $a_0$ and yields a quantitative method for mapping the detailed variations of $G(a)$ across each individual galaxy as well as on larger and smaller scales. On the opposite end, the large accelerations produced by $G(a)$ appear to be linked to the weak-field limit of the fourth-order theory of conformal Weyl gravity.

An original letter to appear in MNRAS

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Cited by in corpus (8)

• Hints of Modified Gravity in Cosmos and in the Lab?
• Conformal Weyl gravity via two stages of quasinormal ringing and late-time behavior
• Universality of minimal length
• Gauss's Law and the Source for Poisson's Equation in Modified Gravity with Varying G
• Universal expansion with spatially varying $G$
• Unraveling the mystery of the cosmological constant: Does spacetime uncertainty hold the key?
• The modified Newton attraction law and its connection with cosmological $\Lambda$--term
• Bimetric MOND as a framework for variable-$G$ theories -- local systems and cosmology