twin universe cosmology Matter ghost-matter astrophysics.3 : The radiative era : The problem of the "origin" of the universe.
The problem of the homogeneity of the early universe. (p4)
In the matter dominated region, these quantities are » constants ». In order to link these two eras, let us write
(73)
where J(r) is the function :
where r_c r is a critical value of the density, corresponding to an epoch earlier, but close to the decoupling phenomenon.
It is clear that when r << r_c r, the constants tend towards absolute constants. When r >> r_c r, they follow the laws (72)
When r << r_c r after matter-radiation decoupling : r @ r_m
(74)
When r >> r_c r before matter-radiation decoupling : r @ r_r
(74bis)
We can examine the variations of the constants before decoupling. Introduce :
(74ter)
which corresponds to the variation of the matter energy density r with respect to the chosen time-marker (in its non-dimensional form). We assume that t = 1 corresponds to that critical time (when r = r_c r), which is supposed to occur before the decoupling time. We then obtain :
(75)
G_o, m_o, h_o, c_o, and e_o correspond to the current values of the constants (t >> 1 and r << r_c r). We obtain the following curves :
** ** Fig. 2 : Evolution of the gravitational constant G during the radiative era.
** ** Fig. 3** : Evolution of the speed of light during the radiative era.**
