Observable signatures of precanonical quantum gravity

Precanonical quantization of general relativity describes the quantum geometry of spacetime as a spin connection foam (SCF) and predicts observable signatures: an invariant acceleration $a_* = 8\,\pi \hbar G \varkappa $ and a cosmological constant $\Lambda \sim a_*^{2}$ . Their small values are attributed to the hadronic scale of the parameter ϰ, introduced on dimensional grounds and related to the mass gap in the Yang-Mills sector of the Standard Model. By considering a test particle moving in the gravitational field of a point mass M immersed in a static SCF background, we obtain a modification of the Newtonian potential $\Phi (r) = - \frac {GM}{r}\, {}_{2}F_{1} (-\frac12,-\frac14;\frac34;- \frac { a_*^{2} r^{4}}{2 G^{2}M^{2}})$ and recover MOND as an effective description in the mean-field of fluctuating accelerations in SCF. Estimations suggest that the SCF corrections are potentially detectable in tabletop experiments, manifest themselves in the MONDian dynamics of flat galactic rotation curves, and may influence the dynamics of the Öpik-Oort cloud and the formation of large-scale structures in the Universe.