Dynamics of the Laplace-Runge-Lenz vector in the quantum-corrected Newton gravity

TL;DR

This paper investigates how quantum corrections to Newtonian gravity affect galactic rotation curves and the dynamics of the Laplace-Runge-Lenz vector, revealing a strong mass-dependence of the correction parameter.

Contribution

It provides a calculation of the upper bound for quantum correction parameters at smaller scales using the Laplace-Runge-Lenz vector dynamics, highlighting their mass dependence.

Findings

Quantum corrections can explain galactic rotation curves without dark matter.

The upper bound on quantum correction parameters is very restrictive.

The correction parameter $al u$ strongly depends on the mass of the system.

Abstract

Recently it was shown that quantum corrections to the Newton potential can explain the rotation curves in spiral galaxies without introducing the Dark Matter halo. The unique phenomenological parameter $\al\nu$ of the theory grows with the mass of the galaxy. In order to better investigate the mass-dependence of $\al\nu$ one needs to check the upper bound for $\al\nu$ at a smaller scale. Here we perform the corresponding calculation by analyzing the dynamics of the Laplace-Runge-Lenz vector. The resulting limitation on quantum corrections is quite severe, suggesting a strong mass-dependence of $\al\nu$.