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A word about the parallax method:
This method was introduced by the German astronomer Bessel. On the left, the orbit of the Earth. S: the Sun. s: a star.
From two opposite points of view on the Earth's orbit (T1 and T2, for example corresponding to July to December), the star s occupies two different positions with respect to very distant stars, which form the background.
The astronomer can then calculate the angle Δq and easily determine the distance D to the star using the following formula:
(108 ter)
The problem of the early universe.
Consider a time close to what is called the "initial singularity": t = 0.
Assume that at this "very beginning of the universe", a test particle emits an electromagnetic wave, which propagates at the speed of light c. After a time t, this wave forms a sphere whose radius is ct. It is usually called the cosmological horizon. For a particle to be "informed" by another particle, the latter must be located within its spherical horizon.
The expansion dilates the cosmic "material", that is, space itself. One can consider two particles called comoving, that is, "which move with space".
Let R(t) be a characteristic length describing the expansion of space.
(109)
It may represent the distance between these two particles. If we compare R(t) to ct, we obtain the following figure (110):
(110)
If t < th, the radius of the spherical horizon is smaller than the average distance between two neighboring particles. They cannot exchange anything (energy, information), they are ignorant of each other: a completely autistic universe, shown in figure (111).
When t > th, the situation changes: the particles can then communicate, because ct becomes much larger than the average distance between them.
The case t < th corresponds to the early universe. The 2.7 K cosmic background radiation (CBR) is the fossil image of this early 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 can persist for a long time over a short distance; collisions will smooth it out quickly.
If you speak the same language as your interlocutor, it is because your ancestors spoke a lot together. Why do the components of this early universe appear so similar, when "they did not communicate with each other in the past"?
The current answer is called inflation, a theory developed by the Russian physicist Linde. It amounts to attributing to the early universe a sort of super cosmological constant, varying over time, a sort of repulsive property of the vacuum, causing a fantastic expansion.
In:
J.P. Petit & P. Midy: Astrophysics of Matter and Ghost Matter, 3: The Radiative Era: The Problem of the "Singularity" 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, "near the singularity"?
When we go back in time, the temperature of the cosmic fluid increases continuously. The thermal velocity of particles with non-zero mass also increases and tends toward c as the temperature tends toward infinity.
Particles with non-zero mass have a "proper time":
(112)
which depends on their velocity v, more precisely on the ratio v/c. When v approaches c, the proper time freezes. How can we imagine a clock under such conditions?
We see that the Standard Model is far from perfect in answering all questions (this is not an exhaustive analysis).
In the following, we will present our own works. We first need to introduce some geometric concepts, on which these works will be based.