Physical Applicability of Self Gravitating Isothermal Sphere Equilibrium Theory V Quantized Dark Matter Mass Densities Gravitational Quantization from Λ Why Einstein’s Cosmological Constant is Essential Steady State Stabilised Galactic Halos

Using a new isothermal gravity equilibrium theory, the dust universe model together with a cosmological Schrödinger equation are applied to solving the problem of generating mass spectra. The masses generated can range from sub fundamental particle rest masses to masses greater than that of the universe. The ranges all depend on a quantum integer number l, related to the isotropic index n, which can lie between unity and infinity. One such mass obtained is given by l = 8 and can represent a small galaxy. The rotation curves for stars, in motion, within this galaxy are examined for flatness and found to have gradients of approximately, −10−23. Examination of the Newtonian gravitation potential associated with these mass quanta reveals that it is, consistent with the dust universe model, based on Einstein’s cosmological constant, Λ, rather than on Newton’s gravitational constant, G, as this last constant disappears by fractional cancellation within the theory structure. Thus this quantization of gravity is based on the cosmological constant. There is found within this theory structure a simulation of negative mass from suitably geometrically orientated positive mass. It is suggested that this feature could supply an explanation for the character of dark energy mass as being due to suitably orientated positive mass. However, this last point needs further study. This paper is a corrected version involving an added section (8) explaining the corrections.