twin universe missing mass cosmology
*The missing mass problem (p7) *.
Post technical comment.
Section 3: In General Relativity, a link between the field equation and Poisson's equation is established by performing a series expansion (11) of the metric around a Lorentzian metric, this background metric, like the perturbation term, being time-independent. The same procedure is repeated, this time with two populations of densities ρ and ρ*. These questions are treated with greater precision in the article:
J.P. Petit and P. Midy: Matter, ghost matter astrophysics. 1: The geometrical framework. The matter era and Newtonian approximation. [On this site: Geometrical Physics A, 4, 1998, section 4.]
Section 4: Eddington's solution emerges from techniques borrowed from kinetic theory of gases (Vlasov equation). Although the detailed calculations are not provided, the method involving two "joint" stationary solutions is the same.
Section 5: When Pierre Midy performed these first computer simulations, he handled the boundary conditions in a classical manner, a question that will be revisited in the paper:
J.P. Petit, P. Midy and F. Landsheat: Matter, ghost matter astrophysics. 5: Results of numerical 2D simulations. VLS. About a possible schema for galaxies' formation. [ On this site: Geometrical Physics A, 8, 1998, figure 15].
...Here he used a "slow" program, without velocity truncations or Monte Carlo-style sampling. Therefore, all n² interactions were computed laboriously, but the result is thus reliable. In practice, the program stopped whenever an interaction between two point masses produced a trajectory curvature too pronounced. The calculation step was then reduced accordingly, until this issue was resolved. Then the calculation resumed at normal speed. Figure 8 shows the first "emulsions" obtained with these two populations repelling each other.
Section 7: The problem of the invisibility of "twin structures" was then raised. In this article, we took it as an axiom. In classical General Relativity, material objects are assumed to be visible. But in the field equation, no particle appears. It is a macroscopic description of the medium. The astronomer can then say, "The hypothesis is good. The proof is that I can observe the objects optically." At this stage, we had merely stated, in a way, that the invisibility of twin structures could also be taken as an assumption, neither more nor less valid, adding: "If these structures exist, the 'proof' that this hypothesis works is... that we don't see them!"
But subsequently, a better geometric description of the problem (a two-sheeted covering of a manifold) transformed this "physical hypothesis" into a "geometric hypothesis." Since photons are assumed to travel along null geodesics of each sheet, and since these sheets are disjoint, photons cannot pass from one sheet to the other. See paper:
J.P. Petit and P. Midy: Matter, ghost matter astrophysics. 1: The geometrical framework. The matter era and Newtonian approximation. [ On this site: Geometrical Physics A, 4, 1998, section 3.]
Critique of this work.
According to this first model, the universe is supposed to be closed. Spatially speaking, it would then be a 3-sphere S³. The drawings in figures 12 and 13 suggest that matter might, from time to time, form alternately in clumps and in a "lacy network," with transition zones. Immediate objection from an observer:
- Under these conditions, observation at very large distances should reveal such a structure. If galaxies form, in a vast region, a lacy network (Very Large Structure), this tendency should then reverse at large redshifts, where galaxies should instead form large clusters, which is not observed.
Objection retained.
