...We assumed in the previous paper [1] that the Universe had a S3 x R1 geometry. Any region of the universe interacts antigravitationnaly with its associated antipodal region, through equation (1). There is a single kind of positive matter m, filling the S3 sphere. Then the total mass of the Universe is non-zero. In the reference [1] several didactic 2d images (figures 10, 11 and 12) were given, in order to explain the mechanims of the interaction of the two adjacent folds.
...Using a boosted HP work-station and a set of 2 x 5000 interacting points, F.Lansheat confirmed the work of Pierre Midy (reference [1] , figure 8) . Then he focussed on a smaller region, indicated on the figure 3, in which the density of the matter in the "adjacent fold" was much higher that in the other fold.
As expected the gravitational
instability still occurs and provides new conjugated structures. See figure
4 and 5 .
Figure 4 : Results
of simulations performed by F.Lansheat, showing the large structure of the
Universe, due to the interaction of the two adjacent folds. Mean value of
r*
= 50 times the mean value of r
(left). Left : cellular
structure. Right : cluster structure.
...The matter of the twin fold forms big stable
clumps, which repel the matter of our fold of the universe, this last taking
place in the remnant space. By opposition to the pancake model numerical simulations,
this pattern is fairly non-linear. After its formation, corresponding to the
Jeans time of the high density system (2 109 years)
, there is no significant evolution of the general pattern over a time comparable
to the age of the Universe so that this model could be a good candidate to
explain the observed spongy aspect of our fold of the Universe, at large scale.
3) 2d and 3d simulations.
...From the results of the 2d simulation, F. Lansheat performed a 2 point correlation and compared to the 2d correlation obtained from a grey distribution of points (Poisson distribution). The result is shown on the figure 6. The left hand of the curve is not relevant, for the distance between the points becomes comparable to the mean distance of the random distribution. The growth on the right hand is just an artefact due to the border of the field (periodic boudary). This result cannot be compared directly to the empirical law derived from observational data (slope -1.8), see the surveys of Bahcall (1988) [31], Bahcall and Soneira (1983) [32], Bahcall and West (1992) [33], Luo and Schramm (1992) [34]. Three-dimensional simulations have to be performed, with a larger number of points. If possible, the fitting with the observational data would provide the ratio of the mass densities of the two universes.
...How to outline a scenario for the formation of large-scale cosmological structure in this model ? As long as the coupling between mass and light remains strong (t < 105 years), the Universe remains homogeneous and all the processes linked to the gravitational instability (formation of clumps, galaxies, stars and spongy structure) are frozen. When the Universe becomes transparent we can assume that all these processes occur, with their proper charateristic times of formation and evolution. All that we can say is that the suggested very large structure forms in 2 109 years.
