The missing mass problem (p4)
- The large scale structure of the universe
From equation (24), we see that if a cluster exists in one fold, an associated diffuse halo structure exists in the conjugated region of the second fold. If this model is correct, we should find halo-structures in our fold of the universe. With the help of Dr. Pierre Midy, from the university of Orsay, France, we have performed numerical simulations, using a Cray-1 computer. We consider two distributions of 350 points. The first is represented by little circles and the second by small crosses. At the beginning the points are randomly distributed on the screen and are supposed to represent two uniform gases. Each mass has a random velocity corresponding to an isotropic Maxwellian distribution with an average thermal velocity . Call m1 the elements of the first population and m2 the elements of the second population. We apply Newton's law with:
m1 attracts m1: gravitational effect
m2 attracts m2: gravitational effect
m1 and m2 repel each other: antigravitational effect
We consider this two-dimensional system as periodic in space. In other words, the upper boundary is connected to the lower one and the right to the left (Euclidean 2D torus). Thus, we can calculate the sum of the mutual actions of the particles. For each time interval Δt, we calculate the acceleration of each particle and determine the trajectory by Taylor expansion. Each particle that exits through the right boundary reappears through the left one, and the same applies for the upper and lower boundaries. This makes it possible to study the gravitational instability of these two coupled systems in a finite portion of space (with toroidal topology). The time interval is determined in order to obtain significant computational results. In other words, we require the trajectory of a particle to be approximately regular. The following figures show the typical behavior of the system after 4000 time intervals. In figures 4 and 5, we find both clusters and cellular patterns. This is enhanced in figures 7 and 8.
Fig. 4: Effect of the gravitational instability on system 1
Fig. 5: Effect of the gravitational instability on system 2
Fig 6 (ga3127): Superposition of the two.
Fig 7: Enhanced spatial distribution of the two populations.
Fig 8: White: population 1. Grey: population 2
We suggest that such a mechanism could explain the large scale structure of the universe and the observed distribution of galaxies. Suppose that our fold of the universe corresponds to population 1. In the lower right part of the screen, this matter is arranged around large "empty" bubbles. These bubbles correspond to a cluster arrangement in population 2, supposed to be located in the second fold of the universe (in fact the antipodal region), according to our theory. However, as seen on figure 8, for a given population, the matter can be arranged in some places like a Swiss "gruyère" cheese and in other places like an emulsion.
These first crude numerical simulations need to be developed with a larger number of points and in a three-dimensional representation. We know that the behavior of a three-dimensional system can be somewhat different from that of a two-dimensional one. However, we expect the conclusions to be similar. We think that with a larger number of points, we could obtain a fractal system, as suggested in figure 14, but we emphasize that this particular calculation has not yet been performed, although it is under study. According to this idea, the galaxies should be located in the holes of the associated antimatter cloud, which would ensure their confinement, as suggested earlier.