Effects of Quantum Spin-Connection Foam in the Solar System, Galaxies, and the Universe

Abstract

We argue that effects of the quantum spin-connection foam, which describes quantum gravity according to the precanonical quantization of General Relativity, may already be observed in the form of the small cosmological constant and a modification of Newtonian dynamics at small accelerations, manifested in the flat rotation curves of galaxies. We obtain a modification of the Newtonian potential that takes into account the existence of a fundamental small acceleration scale, $a_* = 8\pi G\hbar\varkappa$, where $\varkappa$ is a parameter with the dimensions of inverse spatial volume that appears on dimensional grounds. The connection between $\varkappa$ and the hadronic scale of the mass gap in the pure Yang-Mills sector of the Standard Model leads to an estimated value of $a_*$ compatible with the Milgromian acceleration scale in MOND. The connection between $a_*^2$ and the cosmological constant leads to a realistic value of the latter. Milgromian MOND, together with a theoretically distinct interpolating function, is derived under the assumption that classical dynamics is modified by the mean-field acceleration calculated from the simplest solution of precanonical quantum gravity in the nonrelativistic approximation. We also indicate that the effects of Newtonian dynamics modified by the spin-connection foam may be observable in the Solar System and even in laboratory experiments.