Variable Modified Newtonian Mechanics II: Baryonic Tully Fisher Relation
  Recently we find a single-metric solution for a point mass residing in an
expanding universe \cite{wong}, which apart from the Newtonian acceleration,
gives rise to an additional MOND-like acceleration in which the MOND
acceleration $a_0$ is replaced by the cosmological acceleration. We study a
Milky Way size protogalactic cloud in this acceleration, in which the growth of
angular momentum can lead to an end of the over-density growth. Within
realistic redshifts, the over-density stops growing at a value where the
MOND-like acceleration dominates over Newton and the outer mass shell
rotational velocity obeys the Baryonic Tully Fisher Relation (BTFR) with a
smaller MOND acceleration. As the outer mass shell shrinks to a few scale
length distances, the rotational velocity BTFR persists due to the conservation
of angular momentum and the MOND acceleration grows to the phenomenological
MOND acceleration value $a_0$ at late time.
