Modifications of Newtonian dynamics from higher moments of quantum spin connection in precanonical quantum gravity

TL;DR

This paper extends quantum gravity models to include higher moments of the spin connection, resulting in more general modifications to Newtonian dynamics and a new low-acceleration regime with nearly flat galactic rotation curves.

Contribution

It introduces higher moments of the geodesic equation in precanonical quantum gravity, leading to generalized MOND-like modifications and a novel low-acceleration behavior.

Findings

Derived quantum-modified Newtonian potentials using hypergeometric functions

Developed steeper MOND interpolating functions

Proposed a new low-acceleration modification with near-flat rotation curves

Abstract

Building upon previous work that derived an alternative to (galactic) dark matter in the form of Modified Newtonian Dynamics (MOND), with a specific theoretical interpolating function, from the motion of a non-relativistic test particle in the gravitational field of a point mass immersed in the non-relativistic static limit of the spin connection foam -- which represents the quantum analogue of Minkowski spacetime within precanonical quantum gravity -- we now show the consequences of using higher moments (third and fourth) of the corresponding geodesic equation with a random spin connection term. These higher moments lead to more general quantum modifications of the Newtonian potential (qMOND potentials expressed in terms of Gauss and Appell hypergeometric functions), more general (steeper) MOND interpolating functions, and a new modification of MOND at low accelerations (mMOND) that features an almost-flat asymptotic rotation curve $\propto r^{-1/18}$, which is expected to operate at approximately the same galactic scales as MOND.