Twin Universe Cosmology
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****The complete file, in pdf, compiled by a reader, Alain Schamp (December 2007)
The problem of the age of the universe.
...Of course, we try to logically link these different works. Arguments related to the description of the evolution of these two twin universes, for example, lead us to the conclusion that the average density of ghost matter must be greater than that of ordinary matter.
...To "treat" the system of two coupled field equations, we describe the two sheets of the universe using so-called Robertson-Walker metrics. This is the Riemannian metric that incorporates the two assumptions of homogeneity and isotropy, and it is precisely this metric that, in the case of a single universe, leads to the Friedmann solutions.
...We introduce two scale factors, R(t) and R(t). These are the characteristic dimensions associated with each of the two universes.
...The problem concerns the initial conditions. We assume "at the very beginning" (although this term will be later reconsidered and discussed) the parameters of the two universes are identical (r = r*, p = p*). Under these conditions T = T* and the field equations become:
S = S* = 0
The solution is then:
R = R* = ct
A linear expansion in both universes.
...Immediate objection: what about nucleosynthesis, the synthesis of helium, for example? A linear expansion would be much too slow. If we go back in time, as in the standard model, we reach conditions where the temperature is sufficient to allow the fusion of hydrogen into helium (and ghost-hydrogen into ghost-helium).
...In the standard model, the Friedman model is the rapidity of the expansion, in the primordial phase, which freezes the reaction and prevents all hydrogen from being converted into helium.
...We will reserve answering this question for later, simply stating that the mode of evolution differs depending on whether matter or radiation dominates. Let us first focus on the "matter phase," when the contribution of radiation becomes negligible (in the standard model, this corresponds to t = 500,000 years).
...It is then shown that this linear expansion mode R = R* = ct is unstable. One of the two universes sees its expansion accelerate, while it slows down in the other. [See on the site: Geometrical Physics A, 4, 1998, section 2.]
...We suppose that it is our own universe that sees its expansion accelerate.
...We have seen above that the Hubble constant is linked to the tangent of the curve R(t). In the standard model, with the cosmological constant taken to be zero:
With this new model, we have:
...The dashed line corresponds to the standard model curve. Compared to this, we note an aging of the universe. In fact, in this instability of the two joint expansions, the phantom universe behaves as if it were propelling ours forward, while in turn, it is slowed down by ours.
...The ghost universe behaves... like a cosmological constant. Its effect is similar to this mysterious "repulsive power of the vacuum."
...There was a time when many people believed that mercury rose in barometers because nature abhorred a vacuum.
Today, the vacuum is no longer abhorrent: it has become repulsive.
...This theory of two interacting universes provides an interpretation that has the advantage of being less esoteric, as no one knows what the horror of the vacuum is. Nevertheless, the universe that tends to accelerate remains fairly close to the linear law, which means that one can consider a fairly wide range of expansion scenarios that would fit with the problem of the age of the oldest stars in our galaxy.
...How to choose between one or another scenario of joint expansions R(t) and R*(t), linked through two coupled differential equations? [See on the site: equations (37-a) and (37-b) of Geometrical Physics A, 4, 1998.]
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