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The entire 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 lead us, for example, to the conclusion that the average density of ghost matter must be higher than that of matter.
To "treat" the system of the two coupled field equations, we describe the two sheets of the universe by so-called Robertson Walker metrics. This is the Riemannian metric that incorporates the two hypotheses of homogeneity and isotropy, so it is this one, in the case of a single universe, that leads to Friedmann's solutions.
We introduce two scale factors
R(t) and R*(t).
These are the characteristic dimensions related to each of the two universes.
The problem concerns the initial conditions. It is assumed that "at the very beginning" (but this word will be later taken up and commented on) 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 arrive at conditions where the temperature is sufficient to correspond to 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 early phase, that freezes the reaction and prevents all the hydrogen from being converted into helium.
Let us reserve the answer to this question for later, simply stating that the mode of evolution is different depending on whether matter or radiation dominates. Let us first deal with 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 mode of linear expansion
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 assume that it is our own universe that sees its expansion accelerate.
We have seen above that the Hubble constant is related to the tangent to the curve R(t). In the standard model, with a cosmological constant taken equal to zero:
With this new model, we have:
In dashed line the curve that would correspond to the standard model. It is noted, compared to it, an aging of the universe. In fact, in this instability of the two joint expansions, the ghost universe behaves as if it were propelling ours forward, while, on the contrary, it slows ours down.
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 had an aversion to the vacuum.
Today, the vacuum is no longer terrible: it has become repulsive.
This theory of two interacting universes provides an interpretation that has the advantage of being less esoteric, no one knowing what the aversion to the vacuum is.
That said, the universe that tends to accelerate remains quite close to the linear law, which makes it possible to consider a fairly wide range of expansion scenarios that would fit with this problem of the age of the oldest stars in our galaxy.
How to choose between such or such a scenario of joint expansions
R(t)
and
R*(t)
, linked through two coupled differential equations?
[See on the site:
the equations (37-a) and (37-b) of Geometrical Physics A,
4,
1998.]
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