a202 A cosmological model: The twin big bang. (p.2)
VLS: The very large structure of the universe.
...As shown in our works, the joint evolution of the two universes is not identical. The ghost universe has a higher mass density r* and a higher temperature T*. We decided to study joint gravitational instabilities in such a mixture, where, as we recall:
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m attracts m (Newton's law)
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m* attracts m* (Newton's law)
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m and m* repel each other (« anti-Newton » law).
A few words about gravitational instability (Jeans instability).
...Consider a single population, a set of masses m. This medium has a mass density r. It also has a (mean) thermal velocity Vth.
...Assume that somewhere in space, we have a region whose characteristic scale is f, where the density is higher. See figure (147).
(147)
...The thermal velocity tends to dissipate this mass concentration, and the corresponding characteristic dispersion time is:
(148)
...Imagine now that this thermal velocity is zero. This clump tends to collapse. One can compute the characteristic collapse time:
(149)
...On the other hand, any clump tends to attract surrounding matter and to grow. This perturbation will grow if the characteristic accretion time (characteristic collapse time) is smaller than the dispersion time. :
(150)
We find a characteristic length :
(150-a)
called Jeans' length.
...Any mass-concentration whose span is larger than this characteristic Jeans' length will grow and form clumps. Smaller ones will dissipate.
...When a clump of matter forms, it is warmed, which increases the internal pressure force. Finally, internal pressure stops the process.
...One could think that gravitational instability, Jeans instability, forms galaxies, stars, and so on. But this is not so simple. For example, in the Standard Model, when t < 500,000 years, the temperature of the mixed matter and radiation is higher than 3000°K. Then matter (75% hydrogen, 25% helium) is fully ionized.
...Radiation, electromagnetic waves, cross ionized gases with great difficulty. When an astronaut is in the re-entry process, his spaceship is surrounded by hot, fully ionized gas for several minutes. Then no radio-communication is possible because electromagnetic waves cannot cross the shell of ionized gas which surrounds his ship.
...A light ray is an electromagnetic wave. It acts on free electrons, not on bound electrons. An ionized gas contains many free electrons. A neutral gas, none. That's why when the Universe is warm and ionized, radiation and matter are strongly coupled.
...In matter, the absolute temperature Tm is the measure of the thermal velocity :
(150-b)
where k is the Boltzmann constant (k = 1.38 × 10⁻²³).
When :
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Matter and radiation are closely coupled
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Radiation dominates (Standard model t < 500,000 years)
then :
(150-c)
but :
(150-d)
The Jeans length obeys :
(150-e)
...The last corresponds to the mass-conservation requirement, during the expansion process R(t). We see that the Jeans length varies like R(t). So, the younger the universe, the smaller the size of the clumps which would tend to form.
...When t < 500,000 years, the radiation prevents the clumps from forming. But, immediately after decoupling, matter clumps can form. Let us compute their mass. It is :
(150-f)
...i.e.: 100,000 solar masses (the typical mass of a globular cluster).
...According to this scheme, the globular clusters would form first, just after decoupling. The galaxies, considered as sets of such clusters, would appear after, and so on....
...But all this occurs in a rapidly expanding universe. We don't know how to compute it, to describe gravitational instability in an expanding universe. Furthermore, we don't know how to define Newton's law in an expanding universe.
...As a conclusion, we have several schemes for the birth of galaxies. Some believe that stars form first, then galaxies. Others have the inverse opinion ...
...Following this general idea of hierarchical structure, people thought that, if galaxies were organized into clusters of galaxies (Coma, Virgo), at larger scales these clusters should belong to some super-clusters. But the observations (1977) revealed a completely different structure. See figure (151):
(151)
...The galaxies were arranged around large voids (typically 100 light-years in size). At a very large scale (VLS), the universe looks like joined soap bubbles. The clusters of galaxies correspond to the intersection points of three "folds". See figure (152).
...Today, it is still difficult to explain such structures. Following the initial idea of the Russian Zel'dovich, Mellot carried out 3D numerical simulations. But the obtained cells were not stable in time. They vanished rapidly, except if one stabilizes the system with an ad hoc cold dark matter distribution.
...The model matter-repulsive ghost matter gives an alternative interpretation of the phenomenon. See our paper :
J.P. Petit, P. Midy and F. Landsheat: Astrophysics matter-matter ghost. 5: Results of numerical 2D simulations. VLS. About a possible scheme for the formation of galaxies. Physical Geometry A, 8, 1998.