MOND-like acceleration in integrable Weyl geometric gravity

Understand

In this paper a Weyl geometric scalar tensor theory of gravity with scalar field $\Phi$ and scale invariant cubic ("aquadratic") kinetic Lagrangian is introduced.

• Einstein gauge (comparable to Einstein frame in Jordan-Brans-Dicke theory) is most natural for studying trajectories.
• In it, the Weylian scale connection induces an additional acceleration which in the weak field, static, low velocity limit acquires the deep MOND form of Milgrom/Bekenstein's gravity.
• The energy momentum of $\Phi$ leads to another add on to Newton acceleration.