Dark Matter and MOND: Two sides of the same coin?

Abstract

It has recently been reported that the application of convolutional neural-network techniques to infer the dark-matter distribution in the local cosmos has revealed how it follows the $D\approx 2$ hierarchical distribution of galaxies in the locality, rather than exhibiting the expected homogeneity throughout the IGM. Taken at face value, this implies that the Hubble Law, observed to be followed on scales which are deep inside the observed hierarchical structures, can no longer be assumed to arise from universal expansion. So, if not universal expansion, then what? As a possibility, it has been recognized for a considerable time that if the lower cut-off scales of a $D \approx 2$ hierarchical cosmos are identified with the scales of a typical galaxy, then gravitational redshift automatically follows the Hubble Law with $H_g \approx 70\,km/sec/Mpc$. Inter alia, this suggests a model of galaxy formation in a $D\approx2$ hierarchical IGM in which all of the material $M_0$ within a sphere $R_0$ coalesces about a unique center so that hierarchical symmetry is broken on the scale $(M_0,R_0)$. Putting these things together leads unambiguously to the conclusion that, in an hierachical cosmos, the Dark Matter hypothesis and Milgrom's MOND hypothesis are two sides of the same coin.