The Cosmological Constant
The Cosmological Constant
The empirical determination of the Universal Gravitational Constant as
G = 6.67 x 10-11 Nm2/r2
and the resulting deduced determination of the intensity or strength of the gravitational field at any point
g = G m 1/r2
is the kind of approach that I feel appropriate to the Cosmological Constant. This approach has given us the practical ability to work with the intensity of the gravitational force at the earth’s surface of about 9.8m/sec2 as the acceleration factor due to gravity and use it to determine the force of a free falling mass and the even more practical notion of weight. By applying this kind of process to the Cosmological Constant and Inflation, I mean that we are dealing with a force that, in broad strokes, fulfils the function of dispersion of the energy that gravitation has concentrated into mass. The balance of course entails the many processes that we have discussed so far (and probably many more). Removing these two driving entities from the Galactic Energy Cycle and opposing them directly, we have to find equivalence between the sum of their energy contributions to the cycle and can the perhaps deduce a practical use for the intensity or strength of inflation at any point near a mass.
My suggestion is then that we recognise λ (which is classically known as the Cosmological Constant) as the “inflation factor” which would be related to the Cosmological Constant (Λ) in the same way that g is related to G when discussing gravity. This gives the local variable “inflation factor” (λ) the freedom to vary in strength due to various factors like the distance from mass and the size of the mass.
This Universal Inflation Constant or Cosmological Constant (Λ) we must then find empirically. It may turn out that we have to use a negative number to indicate direction in our already gravity dominated word. It is then this factor that will be used to determine the flatness of the universe as well as the relation between G and Λ according to the formula:
Λ = 8 π G Pv
where Pv is the “vacuum energy” which I would imagine is considered to be a constant denoting the generalisation of the “energy contained in a vacuum”.
I would however like to extend this different approach in the light of the separation of λ and Λ in this article and suggest that the (to be) determined constant (Λ) then be used in the calculation of the LOCAL vacuum energy as the local variable “inflation factor” (λ). This measure of the “local inflation intensity” at any point in space would be seen as the equivalent of g in its relation to G. For even more fun let’s rather call it the “warp factor”? Yes I like the name “warp factor” (λ) better because (as we will see when discussing relativity) that is really what it’s function will be in cosmology. The formula to determine the warp factor could then be determined locally by the formula
λ = Λ m/r2
where m is the mass of the black hole and r is the distance from black hole of the point in space for which we are trying to determine the warpedness. This mass could refer to any massive body and the mass of the earth of course is insignificant compared to a black hole for instance. Our local experience of “λ” or warp factor is very small but on a galactic basis it is a large enough factor to keep replacing the space and time that gravity is devouring. Note also that the mass factor could become complicated because the inflation (warp factor) at any local point in space is dependent upon the combined gravitational mass in the local vicinity. Of course this could be a resultant mass from many masses like a galaxy where the distance would be determined by their combined gravitational centre.
I would like to repeat that Λ has yet to be determined empirically and until this is done through careful measurement the actual warp factor (λ) relating to our existence cannot be calculated properly. I have however devised a method to approximate this factor by assuming equivalence relationships that Einstein hinted at … but more of this under the section on relativity.
This all this bottom up thinking presupposes that we live in a homeostatically balanced galaxy and universe. However, after my meagre attempt to review the facts and observations we have made as mankind on our tiny planet, this is my conviction.
We thus have to admit that the Earth’s effect on λ is so small that it has such a small effect on our everyday practical living that we could ignore its local effect, BUT, it does mean that we live in a local area of warp. We have to conclude that the position we inhabit in our galaxy lies within a framework of space fabric whose properties of space density (distance and time) is largely determined by the extent to which space has inflated since it left our own black hole. This local inflation intensity or warp factor (“λ” as we have defined it) must then be determined by
λ = Λ m bh/r2
In this case the m bh is the mass of the black hole and r is the distance of the earth from the centre of our galaxy (the black hole) which is about 26 000 light years. We do not know the mass of the black hole at this stage and remembering that all the dark matter, dark energy, other stars, molecular clouds as well as other miscellaneous debris have to come into the calculation, we will not even go there. Some wishful mathematician can rather attempt such a feat. The point is however that when you evaluate the parameters at a certain point in space this λ -factor has to be calculated to ascertain the real values of distance, space and time at that point. This is the essence of General Relativity as I understand it.
The “curvature of space” (as Einstein put it) is an incredible concept but in a way a bit confusing because, as we have explained before, it tries to depict the route that an object would travel through space. This is not a familiar convention for us dummies. We are used to the contour lines on a map joining areas of equal elevation. The space curvature analogy on a map would be lines indicating the steepest path that water would flow or a ball would roll. Generally this would be at right angles to the contour lines … a practical but certainly more complicated view!! I would like to suggest that without discarding the “curvature of space” we add the more intuitive “warp factor” that we have discussed here to take this concept to a deeper level of iso-density contours. I will come back to this concept when we discuss relativity because one more big hairy beast called “time” has to be weaved into our vocabulary before we can get the most out of relativity and the warp factor.
