twin universe cosmology

Twin Universes cosmology (p 9)

10) The problem of the cosmological horizon.

...Clasically this the cosmologic horizon is defined as is ct., which arises a paradox. The observed Universe is very homogeneous, at large scale. If we compare any characteristic distance R (t) (for an example the mean distance between particles), with the horizon, we get :

Fig. 17: Comparizon of the evolution of the characteristic length of the Universe with the cosmological horizon, in an Eintein-de Sitter model.

In the present model the cosmological horizon becomes the following integral :

(87)

Fig. 18 : Comparizon of the evolution of the characteristic length R of the Universe with the cosmological horizon, in the present model. They have the same variation in time.

...If the Universe was homogeneous at the begining, the collisional process, always present, tends to maintain this homogeneity. It it was not, it tends to smooth it. This constitues an alternative to the theory of inflation.

...This law between R » t²^/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 single observable effect is the red shift..

11) The link with the Robertson-Walker geometry.

All this is compatible with the solution (34) if we give the following non-standard definition of the cosmic time :

(88)

The dimension of the constant is :
(88b)

In the standard definition of the cosmic time from

t = constant x° ( x° = ct)

the dimension of the constant is

(88t)

12) Entropy as a better chronological marker.

...The detailed calculation of the entropy per baryon, as defined by :

(89)

where f is the velocity distribution function, was given in a former paper, with "variable constants". See [13] , section 2.
...As a result, we found :

(90)

...If R(t) is an increasing function of t , the cosmic entropy grows like the cosmic time. In lab's experiments we usually relate entropy with time and consider that, according to the second principle, there is no possible strictly isentropic phenomenon. We consider that the time flux depends on the entropy change. In the classical model it is somewhat paradoxal to notice thet such enormous change in time would go with zero entropy variation. In the present model when the time t tends to zero, s tends to - ¥

...We have s = constant Log t . If we change the measure of the entropy (modifying the value of the constant) and write :

(91)

we get :

(92)

dt = 3/2 t ds

Let us return to the Robertson Walker metric.

(92b)

We get, 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 versus the entropy.

...In the classical description (t , s ) the physicist, when t tends to zero, has some difficulty to define any material clock, for the velocities of the particles tend to c. In a "variable constant cosmologic model" the entropy per baryon (99) is no longer constant and never fails to describe the events of the Universe. Notice that in a (s , s) description, the problem of the origin of the Universe falls down. In addition, if we describe the Universe in a phase space (position plus velocity) we found that the associate characteristic hypervolume R³c³ varies like t.