twin universe cosmology ghost-matter astrophysics.3 : The radiative era: the problem of the "origin" of the universe. The problem of the homogeneity of the early universe. (p6)
Fig. 8 : Compared evolutions of temperatures.
- The problem of the origin of the universe.
Corresponding to that new description of the radiative era, the entropy, as shown in former papers ([4], [5] and [6]) is no longer constant.
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For detailed calculation, see reference [6]. As shown in that former paper, if during that radiative era the entropy is chosen as chronological parameter, the metric becomes conformally flat :
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The origin corresponds to s = - ¥ . Note that s, the entropy per baryon, corresponds to the so-called "conformal time" Log t. With that new time-marker, the "initial singularity" disappears.
Looking back in the distant past (early universe), one gets difficulties to define a clock in order to measure time, because all the particles move at relativistic velocities. It becomes questionable to conceive a cold clock. Consider a system of two masses orbiting around their common center of gravity :
Fig. 9 : The basic clock.
We assume that this clock is not destroyed during the expansion process and calculate how many turns occurred in the distant past (from t = tcr to the hypothetical origin of "cosmological time" t = 0). From above :
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R » t 2/3 G » t - 2/3 m » t 2/3
The orbital period, that is the period of the clock, corresponds to
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The number of turns is :
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(which tends to infinity when t1 tends to zero). Surprisingly, we recover the entropy per baryon s. If a rotation of the above system is considered as an event of the evolution of the Universe, there are an infinite number of events between today and the epoch defined by the time marker t = 0.
Compare the universe to a book telling a story. The time is the width of the book. One would like to reach the first page to read what the author's purpose was. Then we try to flip back through the pages of the book. But the relevant question is not the width of the book, but how many pages it contains. A page is an event. According to this new definition of time, when we flip back the pages, they become thinner and thinner: the book has an infinite number of pages, so that reaching the preface becomes hopeless.
- An alternative to the inflation theory.
Classically, the cosmological horizon H is defined as ct, where c is considered as an absolute constant. It raises a paradox, as the early universe is very homogeneous (CMB or cosmic background). If we compare any characteristic distance R(t) (for example the mean distance between particles) with the horizon H, we get :
**Fig. **10 : Comparison of the evolution of the characteristic length of the universe with the cosmological horizon in an Einstein-de Sitter model.
In the present model, the cosmological horizon becomes the following integral :
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**Fig. **11 : Comparison of the evolution of the characteristic length R of the universe with the cosmological horizon, in the radiative era: same temporal evolution.
We get horizon H(t) » R(t) during all the evolution of the universe, so that its homogeneity is ensured during the radiative era. This is an alternative to the theory of inflation (whose only current justification is the present homogeneity of the early universe).
