Variable Modified Newtonian Mechanics III: Milky Way Rotational Curve

TL;DR

This work develops Variable Modified Newtonian Mechanics (VMOND), a cosmology-dependent MOND-like framework, and applies it to Milky Way–mass overdensities that monolithically virialise and flatten into Mestel disks. The model yields a radius- and redshift-dependent MOND scale $a_0^{VM}$ that approaches the canonical $a_0$ at large radii, producing BTFR-consistent velocities and a rotation curve in the $17.7$–$27.3$ kpc range that closely matches Gaia DR3 data for plausible turnaround redshifts ($z_{ta}\approx 24$–$33$). The analysis demonstrates that VMOND can account for galactic mass discrepancies without dark matter while remaining consistent with solar-system and wide-binary constraints, which show negligible deviations from Newtonian predictions. These results support VMOND as a principled, relativistic origin for MOND-like phenomenology at galactic scales, with implications for early structure formation and cosmology.

Abstract

For a point mass residing in an expanding universe, within General Relativity (GR), a new metric [1} is found to lead to a cosmological background dependent MOND-like acceleration in addition to the Newtonian acceleration. In [2], we study the monolithic evolution of a spherical overdensity at recombination in this combined acceleration, called VMOND. Under reasonable relaxation assumptions we find that a massive spherical galaxy with a stable core can from at $z>7$. For galaxy mass $M=10^{10.5}M_{\odot}$ and a realistic initial overdensity, the model late time MOND acceleration $a_0^{VM}(r)$ at radius r takes on values similar to the canonical MOND acceleration $a_0$ at large radius r. In this work, we consider an idealised model of rotating galaxy formation in which a Milky Way mass overdensity under VMOND monolithically evolves into a virialised sphere. We assume that this virialised sphere is given an uniform systematic angular velocity which equilibriates into a flat disk according to Mestel's analysis \cite{mestel}. We apply Mestel to o the Mestel's disk potential due to the flatten virialised sphere under VMOND to calculate the rotational curve at $17.77kpc-27.30kpc$, We find that the model combined acceleration leads to a Baryonic Tully-Fisher Relation (BTFR) with radius dependent acceleration $a_0^{VM}(25kpc)\sim O(a_0)$. The model rotational velocity in the same radius range matches Gaia DR3 measurements very closely.