Variable Modified Newtonian Mechanics I: Single Metric Universe
  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.   1) We show that a reasonable over-density at recombination, normally considered too small without additional mass, is enhanced by the effects of VMOND, sufficiently to permit turnaround and collapse to a tight central region before $z\sim 14$.   2) We consider a Milky Way mass over-density at turnaround radius which picks up a systematic maximum angular momentum per unit mass. When the overdensity radius contracts to galactic disk size, we find that the rotating speed follows the Tully Fisher relation with an acceleration scale that is again close to the 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. One of us (CCW) has already taken these two points of the model further. Here we are concentrating on the basics. 
James C. C. Wong (U. of Hong Kong), Ray J. Rivers (Blackett   Laboratory, Imperial College London)
astro-ph.CO