A comparison of two theories to explain the rotation curves in galaxies without dark matter particles

Abstract

The aim was to demonstrate the possible compatibility between the gravitational theory of Hajdukovic, which depends upon the existence of virtual particle pairs in vacuo, and that of emergent gravity according to Verlinde, and to derive new physical relationships. These theories, which avoid the necessity for postulating dark matter, and necessary, associated concepts are described. Then, assuming the validity of these theories, the following new results are obtained. Assuming a spherical galaxy model, the theories predict approximately the same radial distance from the galactic centre for the onset of enhanced gravitational fields. This agreement is used (1) to show that the virtual particle density of the vacuum at this distance depends only upon the Hubble scale and Planck’s constant, (2) to calculate its value, and (3) to show that the particles consist of closely packed pions.