Cosmology of twin universes (p 9)
- The problem of the cosmological horizon.
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Classically, the cosmological horizon is defined as being ct, which creates a paradox. The observed Universe is very homogeneous on large scales. If we compare a characteristic distance R(t) (for example, the average distance between particles) to the horizon, we obtain:
Figure 17: Comparison of the evolution of the characteristic length of the Universe with the cosmological horizon, in an Einstein-de Sitter model.
In the current model, the cosmological horizon becomes the following integral:
(87)
Figure 18: Comparison of the evolution of the characteristic length R of the Universe with the cosmological horizon, in the current model. They show the same variation over time.
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If the Universe was homogeneous from the beginning, the collisional process, which is always present, tends to maintain this homogeneity. If it was not, it tends to smooth it out. This constitutes an alternative to the inflation theory.
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This law between R
»
t 2 / 3
must not be considered as an expansion process, but as a consequence of the secular variation of the constants of physics, a gauge process, whose only observable effect is the red shift.
- The link with the Robertson-Walker geometry.
All of this is compatible with the solution (34) if we give the following non-standard definition of cosmic time:
(88)
The dimension of the constant is:
(88b)
In the standard definition of cosmic time from
t = constant × x° (x° = ct), the dimension of the constant is
(88t)
- Entropy as a better chronological marker.
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The detailed calculation of the entropy per baryon, as defined by:
(89)
where f is the velocity distribution function, was given in a previous paper, with "variable constants". See [13], section 2.
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As a result, we found:
(90)
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If R(t) is an increasing function of t, the cosmic entropy grows like the cosmic time. In laboratory experiments, we usually associate entropy with time and consider that, according to the second principle, no strictly isentropic phenomenon is possible. We consider that the flow of time depends on the change in entropy. In the classical model, it is somewhat paradoxical to note that such an enormous change in time would be accompanied by zero change in entropy. In the current model, when time t tends to zero, s tends to -∞.
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We have s = constant × Log t. If we change the measure of entropy (modifying the value of the constant) and write:
(91)
we obtain:
(92)
dt = 3/2 t ds
Let us return to the Robertson-Walker metric.
(92b)
We obtain, with R = 3/2 ct:
(93)
In the representation {entropy, space variables}, the metric becomes conformally flat and we have:
Figure 19: The evolution of the curvature radius R of the Universe as a function of entropy.
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In the classical description (t, s), the physicist has some difficulty in defining a material clock when t tends to zero, because the velocities of the particles tend to c. In a "variable constant cosmological model," the entropy per baryon (99) is no longer constant and never fails to describe the events of the Universe. Note that in a (s, s) description, the problem of the origin of the Universe disappears. In addition, if we describe the Universe in a phase space (position plus velocity), we find that the associated characteristic hypervolume R³c³ varies like t.