  A few years ago Baker \cite{baker} proposed a metric which interpolates
smoothly between the Schwarzschild metric at small scales and the
Friedmann-Lema$\hat{i}$tre-Robertson-Walker (FLRW) metric at large scales which
was rejected as incompatible with Newtonian solar system data. Based on the
adiabatic approximation, we find a unique solution within the variants of the
same construction scheme which avoids this problem. In this metric, a MOND-like
non-Newtonian acceleration arises, which we have termed VMOND, where the MOND
acceleration $a_0$ is replaced by a cosmological acceleration which depends on
the background matter density. We give two circumstances in which VMOND mimics
MOND without the need for additional dark matter. \newline
  1) We show that a reasonable overdensity at recombination, normally
considered too small without additional mass, is sufficient to permit
turnaround and collapse to a tight central region before $z\sim 14$. \newline
2) The velocity dispersions of a large mass spherical galaxy can match the
observed profiles, at large distances obeying the Faber-Jackson relation with a
VMOND-like acceleration of comparable values to the phenomenological MOND
acceleration $a_0$. \\ This is not a universal panacea to the problems
encouraging dark matter but, we suggest, presents a new baseline for
calculation.
