I came up with some formulas for determining Ho based on the G of normal matter plus a postulated constant, G’, which either relates to that same matter or to nonG related matter or even to energy.
To determine Ho using G plus G’, one must assume that G (6.67E11 m^3 / kg sec^2) means that the universe is growing by 6.67E11 m^3 per second per second for each kg of G related mass in the universe. In addition one must assume that there is also an additional G’ related mass or energy that is equal to exactly onehalf of the G related mass, i.e., total “mass” equals 67% G related mass plus 33% G’ related mass or energy.
The density of G related matter figures in the formulas, and to determine that density one does not need to know the mass of the universe since mass cancels out in the formula of 2 X mass / mass X age of universe^2 X G (derived from the above assumption about G). The determined density is then multiplied by the volume of a sphere having a radius of one Mpc to yield the mass contained within that sphere. Consecutively multiplying that mass by G and the age of the universe yields the volume of expansion of the sphere per time. By dividing that volume by the surface area of the sphere, one obtains 2/3 Ho. However, cancellations allow that value to be obtained by using the very simple formula of 2 X G / 3 X age of universe in seconds X 3.09E22 meters (=1 Mpc).
If one uses only G, a Ho of about 47 km/s/Mpc and a maximum recession velocity of 2/3 c for a 14 billion year old universe is obtained. That is why G’ is postulated at a value of onehalf G.
Although using G + G’ predicts a Ho of 70 km/s/Mpc for a 14 billion year old universe, it also predicts a falling Ho and a rising G + G' over time, and a G + G’ related "mass" of the universe of about 1.5E+54 kg. I would appreciate both positive and negative comments and any credible information or ideas that support the predictions.
