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A word about the parallax method:
This method was introduced by the German Bessel. On the left, the Earth's orbit. S: the sun. s: a star.
From two opposite viewpoints on the Earth's orbit (T1 and T2 corresponding, for example, to July and December), the star s occupies two different positions relative to very distant stars forming the background.
The astronomer can compute the angle Dq and easily compute the distance D to the star, using:
(108 ter)
The problem of the early universe.
Consider a time close to the so-called "origin": t = 0
Suppose a particle, at this "very beginning of the universe," a test particle emits an electromagnetic wave expanding at the speed of light c. After a time t, this wave is a sphere whose radius is ct. One usually calls it the cosmological horizon. To be "informed" by a particle, a neighboring particle must be located within its spherical horizon.
Expansion dilates the cosmic "material," space. One can consider two particles that are comoving, which "move with space."
Call R(t) a characteristic length describing the dilation of space.
(109)
It may represent the distance between these two particles. If we compare R(t) to ct we get figure (110):
(110)
If t < th the radius of the spherical horizon is smaller than the mean distance between two neighboring particles. They cannot exchange anything (energy, information); they ignore each other: a fully autistic universe, shown in figure (111).
When t > th the situation changes. The particles can communicate because ct >> the mean distance between them.
t < th corresponds to the primeval universe. The 2.7° K cosmic background radiation (cbr) is the fossil image of this primeval universe, which appears remarkably homogeneous. Why?
If the air you breathe is so homogeneous it is because it is collision dominated. No significant temperature gradient could persist for long over a short distance. Collisions would smooth it quickly.
If you speak the same language it is because your ancestors talked a lot together. Why do the components of this primeval universe look so similar when "they did not talk together in the past?"
The answer today is called inflation, the Russian Linde's theory. It is equivalent to giving the primeval universe some sort of super cosmological constant, varying in time, some sort of repulsive property of vacuum, which causes a fantastic expansion.
In:
J.P. Petit & P. Midy: 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. Geometrical Physics A, 6, March 1998
the reader will find an alternative possible explanation.
The problem of the origin of time.
t = 0
`What does it mean? Does it make any sense, "close to the origin"?
When we go back in the past, the temperature of the cosmic fluid grows and grows. The thermal velocity of "non-zero-mass particles" grows too and tends to c when the temperature tends to infinity.
Non-zero-mass particles possess a "proper time":
(112)
which depends on their velocity v, on the ratio v/c. When v tends to c the proper time gets frozen. How can we imagine a clock under such conditions?
We see that the Standard Model is far from perfect at answering all questions (this is not an exhaustive analysis).
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In the following we will present personal works. We first need to introduce some geometric concepts, on which the work will be based.
