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. (p7)
6) Conclusion.
We follow the basic idea: during the matter-dominated era (which is assumed to occur simultaneously for both systems: matter and ghost matter), the quantities {c, G, h, m, e, eo} behave like absolute constants. During the radiative era, they vary in time.
As shown in reference [4], c and G may vary in time. We point out that the transition from the chronological variable x° to cosmic time t is not automatically x° = c₀t, with an absolutely constant speed of light c₀. Systems with x° = c(t)t are possible.
We then search for time variations G(t), c(t), h(t), m(t), e(t), eo(t) that keep all physical equations invariant. We find such variations and show that they yield, for this radiative era, a common evolution law: R(t) = R*(t) ≈ t²/³.
As a consequence, the entropy per baryon is no longer constant and varies as Log t (so-called conformal time). Reformulated in {s, x, y, z} coordinates, the metric becomes conformally flat.
We imagine a basic clock composed of two masses m orbiting around their common center of gravity. We compute how many revolutions have occurred since the "origin of time" t = 0 and find infinity. We conclude that "cosmic time" t is no longer a suitable variable for the radiative era. For this era, s becomes a better chronological variable to describe events. We consider one revolution of our clock as an event. As a conclusion, an infinite number of (microphysics) events occurred in the distant past. If we identify time with events, the universe no longer has a time origin. The "initial singularity" vanishes.
We compute the cosmological horizon and find it varies like R, thus ensuring the homogeneity of the early universe. The inflation theory, with its heavy assumptions, is no longer necessary.
References.
[1] J.P. Petit: The missing mass effect. Il Nuovo Cimento, B, vol. 109, July 1994, pp. 697–710. [1] J.P. Petit, P. Midy and F. Landshecht: Matter ghost matter astrophysics. Astron. and Astrophys. reference...
[2] J.P. Petit, Mod. Phys. Lett. A3 (1988) 1527
[3] J.P. Petit & P. Midy: Matter ghost matter astrophysics. 1: The geometrical framework. The matter era and the Newtonian approximation. Geometrical Physics A, 4, March 1998.
[4] J.P. Petit, Mod. Phys. Lett. A3 (1988) 1733
[5] J.P. Petit, Mod. Phys. Lett. A4 (1989) 2201
[6] Petit J.P.: Twin Universe Cosmology. Astrophysics and Space Science. Astr. and Sp. Sc. 226: 273–307, 1995
[7] J.P. Petit and P. Midy: Matter ghost matter astrophysics. 5: Results of numerical 2D simulations. VLS. About a possible schema for galaxies' formation. Geometrical Physics A, 8, March 1998.
Acknowledgements:
The author thanks Prof. J.M. Souriau for useful advice and comments.
This work is supported by the French CNRS and by the A. Dreyer Brevets et Développement company.
Deposited in sealed envelope at the Académie des Sciences de Paris, 1998.
Commentary.
This work represents a synthesis between two approaches: that of the paper published in Astrophysics and Space Science (article 2 of the sub-site Geometrical Physics), and that developed in paper 3 (Repulsive ghost matter). In that article, the system of two field equations:
(3)
(4)
represented a kind of makeshift solution, whose effect was to reconnect with the standard model during the radiation phase, making the equations then become:
(3')
(4')
that is, effectively, twice the standard model. This allowed for a sufficiently rapid expansion during this phase to freeze nucleosynthesis and produce helium. With a system:
S = c (Tr − T*r)
S* = c (T*r − Tr)
with fixed constants, the expansion (R ≈ R* ≈ t) would then be too slow. All the hydrogen in the universe would be converted into helium.
Returning to the system (3) + (4), this system presented a difficulty, a problem raised with great relevance by the referee of A&A. When photons transformed into matter and vice versa (as specified in the article), their contribution to the field changed sign, which was hard to justify at the time.
The recourse to a model with variable constants, for the radiation phase, then provided a globally coherent solution. Anyway, whether this model holds or not, there remains a rather strange property: that all known equations of our physics are invariant under the generalized gauge transformation proposed. One must understand the field equation (even if restricted to Einstein's equation), the complete Maxwell equations, and the Schrödinger equation.
It has often been stated that physical constants cannot vary, because even a minimal variation in any one of them would immediately lead to physical impossibilities. True. But this is not about changing just one or a few constants, but all of them simultaneously.
Measurement instruments are built using the equations of physics and their "constants." If one considers such a gauge phenomenon, with these joint variations of all constants, it becomes impossible to detect this phenomenon in the laboratory, since the instruments themselves evolve at the same time as the phenomenon they are supposed to detect. This is equivalent to trying to detect a temperature variation by measuring the elongation of an iron rod with a ruler made of the same metal. I know this is a point that people often find very hard to understand, and even harder to accept.
Of course, this description of the radiation phase is also just a sketch. It does not account for the weak interaction or the strong interaction. To extend this further, one would need to imagine other laws of variation of constants related to these domains. Incidentally, in this strange model, Planck time varies as t and Planck length as R, thus pushing the "quantum barrier" further away as we approach the initial moment t = 0. A strange phenomenon that would require interpretation.
But these works are far from complete. Perhaps we should consider all this as a kind of manifesto. Personally, I believe our ideas about cosmic genesis will need to change significantly in the coming years or decades. And by stubbornly trying to reach back into that fiery past with our still primitive theoretical tools, we end up in a kind of organized schizophrenia. I think, for example, of Linde's inflation theory: a theory justified solely by the need to explain the homogeneity of the early universe, which everyone seems to accept.
Some believe our current worldview, through the standard model, is nearing completion and that only minor adjustments will be needed to finish the edifice. I am not so sure. I think the coming decades may reveal many surprises, offering us a completely different description of cosmic genesis (and I do not claim, by doing so, that my approach represents progress in this sense). Throughout history, humans have always believed their understanding of the universe was nearing completion. Before the breakthrough at the beginning of the century, many eminent people wrote: "Now, we only need to add more decimals to our calculations."
I once read in a book devoted to the m...