Replicating MOND In A Spin-Foam Model

Spin-foam is a quantum gravity approach that quantizes space-time, rather than treating gravity as a separate force with a carrier boson comparable to a photon or a gluon.

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∗ = 8πGℏϰ, where ϰ is a parameter with the dimensions of inverse spatial volume that appears on dimensional grounds. The connection between ϰ 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.

Igor V. Kanatchikov, Valery A. Kholodnyi, "Effects of Quantum Spin-Connection Foam in the Solar System, Galaxies, and the Universe" arXiv:2608.12404 (August 11, 2026) (The Seventeenth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories, Pescara 7-12 July 2024, edited by G. Vereshchagin and R. Ruffini, this https URL, October 2026).