The question now is, how does a vacuum exert a force on a mass carrying body? What I would like to propose here is that the vacuum of space is a "negative energy plenum", where each cubic meter of space can accommodate a maximum amount of energy of 8.168-06J, termed the Constant of Accommodation (A). This essentially means that the vacuum of space has a vacuum energy density (AV) of -8.168-06J/m3, and that space is inclined to be accommodated with the energy held within the matter in order to cancel out these energies and give a zero value. This inclination manifests itself as a partial force (measured in N(1/2)) determined by the constant of proportionality AF.

The important point to note here is that this approach requires that mass carrying bodies do not occupy space, but rather exist within their own spatially extended dimensions. This is something that Einstein thought significant when he stated in Relativity:

"Physical objects are not in space, but these objects are spatially extended. In this way, the concept of empty space loses its meaning" [1]

In response to this I would say that empty space is the volume of space that was previously occupied by energy but which, due to the propagation of matter, has now been vacated. From this, we should deduce that there is a corresponding amount of energy (A) in the observable universe for every cubic meter of space (or conversely, every cubic meter of space can only accommodate 8.168-06J of energy (A), which in turn suggests a vacuum energy density (AV) of -8.168-06J/m3. If this is true, then we should be able to calculate a rough estimate of the Critical Mass Density (CMD) simply by using the constant A (derived form the gravitational constant), and the approximate volume of the universe.

According to WMAP[2], the radius of the observable universe is 13.7 billion light years, giving an approximate radius of 1.29612007526m. Given that the universe is uniform in all directions, an accurate way to calculate its volume would be to calculate the volume of a sphere with radius Ru:

Vu = (4/3Ï€) x Ru3

Vu = 4.188790205 x Ru3 (where Ru = 1.29612007526 m)

Vu = 4.188790205 x (1.29612007526m)3 = 9.12061914678 m3

From here, two equations are needed to find the mass of the universe. The first shows the equation for finding the energy in the universe (Eu), while the second converts the units of measurement from joules to kilograms, and thus from energy into matter.

Eu = Vu x A

Eu = 9.12061914678 m3 x 8.168843247-06J/m3

Eu = 7.45049081273J
The solution to this equation states that the amount of energy in the universe should be equal to 7.45049081273J. All that is left to do now is to convert this into mass to give a rough approximation of the amount of matter in the observable universe (Mu):
Mu = Eu / C2

Mu = 7.45049081273J / 8.98755178716m/s

Mu = 8.2897890256kg

This calculation assumes that all energy within the universe exists in mass form, which is clearly not the case, but the value 8.2897890256kg does give a good indication of the absolute maximum amount of matter in our 13.7 billion year old observable universe. From this information, it should also be possible to ascertain the critical density of the universe. If we accept that the constant of accommodation, A, sets the energy density of the universe at 8.168843247-06J/m3 then the calculation for the critical density of the universe should be:

A/C2 = 8.168843247-06J/m3 / 8.98755178716m/s = 9.089063897-23kg/m3

or

9.086063897-28g/cm3

This value is slightly lower that the 1 x 10-29g/cm3 that seems to be the general consensus for the value of the critical mass density (CMD) of the universe. The most important point to take from this rudimentary calculation is that G, A, AV and the CMD of the universe are inextricably linked. The value given for the CMD of 9.086063897-28g/cm3 should also be viewed as a maximum value, given the fact that it is based upon the notion of all the energy in the universe existing in matter form.

In practice, the only way to measure the values of A, AF, AV and the critical density is with more accurate measurements of G, but with the knowledge of what G actually is (G is the square of the constant of proportionality of the force of the vacuum, AF), the accommodation constants may provide, within a classical framework, a deeper understanding when it comes to grand unified theories and theories of quantum gravity.