Dark énergy (annex 1)
In this annex i give a mathématical indication of the importance of my version on the dark énergy.
We can see the basis text(darkenergy.htm) at the next web address:
http://www3.sympatico.ca/pierrejsavard/darkenergy.htm

First we must do a link between gravitational énergy and dark énergy for contraction zone(galaxy heap) and expansion zone;
as there is a link between the expansion zone(round the contraction zone) and the contraction of contraction zone,because at some
distance from contraction zone centre,the gravitational strength is équal to the responsible dark énergy,that this suggest that dark énergy
responsible  of expansion round the contraction zone wil be the same order of height (in absolute) as the variation of the gravitational énergy
of the contraction zone, we have only to consider the term that représent the gravitational énergy from one contraction zone and for
mathématical comparison, i am only going consider the speed v at power 2 or (v.v),nécessary for the libération of the contraction zone,
because this value give us a idéa of the libération énergy by mass unity(by kilogramme).

Next we must représent the libération speed at power 2 or  (v.v) for our Universe that have some estimate radius,then we have only
to do comparison of this Universe with all the contraction zone and we do this as the following way:
Write R the estimate radius of the Universe and R/N  the mean radius of a contraction zone, N is équal to the ratio of estimate radius
of Universe to the one of a estimatate mean contraction zone, or R/(R/N) = N
With this value, here is the comparison between the v.v of libération for the estimate Universe and one mean estimate contraction zone:
2GM/R   (for estimate Universe)   and  2G[M/(N^3)]/(R/N) = 2GM/[(N^2)R]  for the mean estimate contraction zone
N^3  signify N.N.N or NxNxN  and N^2  signify N.N
then we have 2GM/R with the comparison with 2GM/[(N^2)R]
the term that représent the contraction zone is more little as 1/(N^2)
We have now to consider the sum of contraction zone and do the comparison with the corresponding value for Universe and for do this sum
we have only to multiply by N^3  the corresponding term to the one of contraction zone:

{2GM/[(N^2)R]}(N^3) = 2GMN/R for all the contraction zone compare to 2GM/R  for Universe

The contribution of all the contraction zone is then more that a value of N  to the term 2GM/R and as if the contribution of all the contraction zone
was only 2GM/R , there was also expansion , this when we consider distinct density of space for expansion zone compare to contraction zone.
As we multiply the term 2GM/R by N , this make my version of dark énergy very important and the more N  is great the more my version is important.

I give a example for help to représent the meaning of this comparison:
If a density space in a contraction zone is 8 time more that the density of the round expansion zone, this in a long time could do a increase of space volume about seven time for the expansion zone round of this contraction zone(contraction of half by example), in a other side if we consider a radius of Universe of about 30 milliard light years and if we consider a mean radius for a contraction zone of 500 million light years for a mean contraction zone
(notice that the Great Attractor zone have perhap a radius like that),then we have:
30/(1/2) = 60 = N  and the increase of the volume of Universe would be by the product of 60 by 7 or 60(7) = 420 , the cube(the power 1/3) of 420
that is about 7.5 , this is a possible increase of the radius of Universe that could follow the contraction of contraction zone(contraction of about half
that have perhap already be do for now and this contraction is make again with accélération and for this is the explanation for the accélération of the
expansion of Universe).
If by example this figures as correct, the radius of the Universe would be increase of 7.5 time from  there are hight heap of galaxy that do contraction zone.
But before there are galaxy, there can be have also a expasion of space volume of Universe, but this expansion is perhaps note be in continute
accélération, this is that do possibly have other expansion time and my dark énergy version point out a important contribution to a expansion time that
is follow again.
Finally we can notice that the Casimir effect have been expérienced succesfully, in 1996 by example Steven Lamoreaux get a uncertainty of 5 % .
The Casimir effect show with no doubt that space witout atom have a énergy density and that différent énergy density produce strenghts and enormous
pressure.
As référence to the contraction zone in wich our galaxy is,here a link(see the bottom web page):
http://villemin.gerard.free.fr/Science/Galaxie.htm