twin universe cosmology Matter-ghost matter astrophysics. 1. The geometrical framework. The matter era and the Newtonian approximation. (p5)
Commentary :
This work is based on the system of two field equations:
(1)
(2)
At the time this text was written, a model describing the radiation era with "varying constants" already existed. However, since the referee of A & A had not commented on this part—covered in paper 6—we preferred to revert to the simpler version (1) + (2). This version obviously allows a connection with the standard model when radiation is negligible, resulting in a model "twice the standard model." But this model suffers from a sign change. Not only does it lose some of its elegance, but it has the following peculiarity: when photons transform into matter and vice versa, or ghost photons transform into a ghost matter–antighost matter pair, their contribution to the field changes sign. The model with varying constants, applied to the radiation era, allows us to return to the original system.
(6)
(7)
But without this sophistication, this system of equations cannot describe the radiation era. Indeed, with varying constants, it yields, for R = R*, the trivial solution R ≈ R* ≈ t. This expansion would then be far too slow—for example, to halt primordial nucleosynthesis, which produces helium from primitive hydrogen, and ghost helium from primitive ghost hydrogen. All matter in our universe would thus be converted into helium.
Analysis of the solution reveals an instability between the two expansions R(t) and R*(t) (using the same time variable). The ghost universe effectively propels our universe forward, behaving, notably, like a kind of "cosmological constant" during passage. This is not the "repulsive power of the vacuum," but rather the "repulsive power of the ghost universe."
The shape of the curves in Figure 1, particularly the ratio R/R*, at a time assumed to be our present, depends entirely on arbitrary choices of initial conditions. Different initial conditions would lead to different R/R* ratios, and consequently different r*/r ratios. This is an ad hoc ratio, designed to match the result obtained in 1994 regarding the Hubble constant. Our model, like the one using the Hubble constant, is also "of variable geometry"—appropriately chosen initial conditions allow for R(t) profiles yielding an increased age of the universe. Thus, in the work indicated, the age of the universe can be multiplied by a factor of 1.6, starting from a Hubble constant of 50, to reach an age of 15 billion years. But today, this seems less urgent. Indeed, analysis of data from the Hipparcos satellite appears to have increased the calibration of Cepheid distances—the gold standard for distance measurement. Conversely, theorists have done their best to shorten the age of the oldest stars in our galaxy, based on the analysis of globular clusters and their relaxation states. Thus, "everything has now fallen into place." Sigh of relief: "the alarm was hot."
Is the matter settled? It's a bit early to say. Nevertheless, if needed, the matter-ghost matter model is available to extend the age of the universe at will, just like the cosmological constant...
