Ho and z from G?



This posting provides some formulas I derived based on a premise that might seem ridiculous to some people, yet many of the calculated values based on that premise are in line with popular thinking.

The premise is that besides other things, the universal gravitational constant, G, (= 6.67E-11m^3/kg/s^2) means that the universe is growing by 6.67E-11 m^3 per second per second for each kg of mass in the universe. Although it is logical that G can be interpreted that way, it does not mean that mass is responsible for expansion of the universe, merely that it is somehow related. Obviously, the first place that one would look for such a relationship is with gravity, for example, a gravitational law that provides a repelling force for masses that are further apart than a certain distance.

Using the stated premise, one can determine the density of the universe at a specific age with the following formula:

Density = 2 X mass / mass X age of universe^2 X G

Notice that mass cancels out, so it is not necessary to supply it to use the formula.

Since density changes with the expansion of the universe, one can use it to determine z at a specific age of the universe in accordance with the basic premise. That can be done by finding the cube root of the quotient of the density of the universe at the desired age divided by the present density (using an assumed age) and then subtracting 1. However, cancellations allow the following formula to be used:

z = ((present age in seconds ^2 / desired age in seconds ^2) ^ 1/3) -1

Ho for any specific time can also be determined by multiplying the density at that time 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 Ho for 1 Mpc. The formulas is:

Ho = density X volume of 1 Mpc sphere X G X age of the universe / sphere surface area

However, cancellations allow Ho to be obtained by using the following very simple formula:

Ho = 2 X 3.09E22 meters (= 1 Mpc) / 3 X age of universe in seconds X Mpc.

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