I apologize for my poor English.
Mainstream article for expansion of space : http://www.mso.anu.edu.au/~charley/p...DavisSciAm.pdf
[ Space Doesn't Expand and New Proof of Hubble's Law ]
After the expansion of universe was observed in the 1920s, physicists and astronomers introduced the concept of "space expands" into physics and many observations and research results were used based on this. However, we can't explain why space expands and why it has a specific velocity and is no observations of expansion of space. This study proves that the expansion of the universe and Hubble's law doesn't result from the expansion of space, but is a dynamical result from the movement of galaxies in space. We could confirm that Hubble's law was always valid when the effect of acceleration was smaller than initial velocity. Also, this shows that cosmological red shift comes out from the Doppler effect of light. Expansion of space was explained that it was related to red shift and scale factor. Therefore, it is influencing many areas of astronomy and cosmology. Therefore, if this discovery is true, all matters related to red shift and scale factor should be reviewed.
By and Hubble in the 1920s, expansion of universe, red shift of the galaxy, and recession velocity based on Earth were observed, scientists introduced the concept of "space expands" into physics to explain this.
Observed cosmological red shift was similar to the Doppler shift which occurs when the light source becomes further away from the observer in space, but it was replaced with the concept that space itself expands.
From the two facts of observation of all distant galaxies receding with Earth in the center and that Earth isn't the center of universe, it is presumed that cosmological red shift isn't Doppler shift of the galaxy moving in space.
Moreover, because scale factor is separated and marked by the solution of field equation and this can be corresponded to expansion of space, it was thought that observed cosmological red shift results from the expansion of space.
A recent study put some other interpretation on the expansion of space.
However, significant matters related to expansion of space haven't been proved or explained during the 80s until today and these results aren't being observed.
1. Expansion of space isn't an obvious matter.
Thinking of space expanding, there are 3 cases.
C. Maintenance - Condition without expansion and contraction
If force does not exists, it is natural that any physical quantity has the same value, so "maintenance" is the most natural value.
2.If space expands, the expansion speed of space can vary from - infinity to + infinity. There is no basis that a specific value among these should be chosen.
3.We have never observed the expansion of space.
The physical meaning of "space expands" is that all space expands.
A. Space between an atomic nucleus and electrons also expands.
B. Space between the Sun and Earth also expands.
C. Space between galaxies also expands.
Like the above content, it means that all space expands.
Scientist who claim expansion of space, space all expands in A, B, C, but
For A, binding is consisted by electromagnetic force, space actually expands but position is compensated by electromagnetic force in time we don't feel, and therefore it is explained that is why we can't observe that effect.
For B, space between the Sun and Earth expands every second, but position is immediately compensated because the Sun and Earth is strongly combined by gravity and explains that is why we can't observe that effect.
On the other hand, for C, space between galaxies also expands, but it is explained that expansion of space appears in C because their gravitational binding is weak.
It is a possible explanation.
However, this is a possible explanation for Hubble's law, but it is clear that we didn't observe the "expansion of space."
Thus, we have never directly observed expansion of space between electrons and protons, and energy loss used in compensation of position was never measured, and was never measured between Earth and Sun either.
4.Expansion of the universe and expansion of space isn't the same concept.
The fact that the universe expands shows that distance between galaxies become further. This can be explained from the expansion of space between galaxies, but this can be explained even when galaxies have +r direction initial speed in condition where space doesn't expand.
5. The metaphor of a balloon is 4 dimensional or 2 dimensional, the observed Hubble's law is an observational matter in 3 dimensional space.
Balloon analogy is just a pedantic metaphor, not a precise explanation.
This study proves that Hubble's law is a natural result from the dynamics of galaxies in 3 dimension and tries to prove the fact that all far away galaxies have recession speed with Earth in the center.
II. Proof of Hubble's law through dynamics
1. After inflation of early universe has almost finished, particles started to have some velocity.
This velocity distribution naturally has higher velocity when it is further away from the center of the universe and has lower velocity when it is closer to the center.
A. Big bang simulation in the zero energy universe
[Video for Big bang Simulation]
Fig.1.Velocity distribution of galaxies at early universe.
Red arrows show the velocity vector of particles. It can be known that the magnitude of velocity vector is bigger as it become further from the center.
Even if the velocity of particles is zero in the early universe, there are particles with higher velocity in further areas from the center and particles close to the center have relatively low velocity by inflation. When positive mass gravitationally contracts to form a galaxy, momentum must be conserved, so higher initial velocity continues to exist as it becomes further away from the center of universe.
B. Natural distribution of velocity in the 3D space
Thinking in another way, 3 dimensional space can be divided into 3 areas (from the center) to far, middle, and close area. Even if the velocity of the far area is lower than the middle area, middle area particles exceed far area particles when time passes because the velocity of middle particles are higher. As a result, velocity distribution of particles shows that the velocity of far areas is highest, middle area is second, and the close area becomes third.
C. Velocity distribution when some kind of anti-gravitational source exists
If some kind of anti-gravitational source in 3 dimension exists, M exists with even density, the above velocity distribution can exist.
If anti-gravitational source is evenly distributed in accelerating expansion time like the inflation of early universe, a bigger acceleration a exists as r becomes larger and velocity distribution has a higher velocity as the radius of the universe becomes larger. As a result, higher velocity exists for particles of far area from the center of the universe after inflation ends.
The 3 explanations shown above mean that higher velocity for larger R(distance from the center of universe) after inflation in the early universe isn't a peculiar phenomenon. If speed in small area in the early universe distributes from 0 to c and if some time passes, velocity distribution will be in order as above.
2. Derivation of Hubble's law in space without expansion
A. Decelerating expansion time
First to look into the possibility of this model, let's look into the case in which the direction of and is the same.
, : It is the speed in which A and B galaxy has when inflation ends.
: Acceleration by force (maybe gravity) occurred from some unknown energy source. It is the acceleration of decelerating expansion because decelerating expansion seems to have taken place in the early universe. It is actually a function of time. To make the problem simple, we plan to solve the problem making it as a constant.
: Total time of universe decelerating expansion.
The above equations are equations of speed and distance when acceleration is constant.
B. Accelerating expansion time
After decelerating expansion ends, there was a time of accelerating expansion. Acceleration is given as this time and the duration time is set as .
, is the now speed of galaxy a and galaxy b.
C. Deriving Hubble's law (when direction is the same)
is the relative speed of galaxy a and galaxy b.
[LaTeX ERROR: Image too big 810x20, max 650x600]
Because the galaxies or particles in the early universe were concentrated in a very close distance,
it can be set as
This is the age of the universe.
Deriving the relation between and ,
It can be known that Hubble's law comes out. WoW!!
Especially, the Hubble constant is H=1/t and this is a result that the Hubble constant in Hubble's law corresponds to the reciprocal of the age of universe. Considering decelerating expansion and accelerating expansion and movement of relative particles, the actual age of the universe is . It is very close to 1.
Therefore, the above model contains simple equation, but has possibility.
Thus, the recession velocity and Hubble's law between galaxies don't come from some vague concept(unknown concept without empirical experience) of "expansion of space" and shows possibility that it comes from a simple movement equation called .
In , if a(t) is small, this is because a shape Hubble's law comes out.
D. The observation of "all galaxies become further from us and all galaxies have recession velocity from Hubble's law" isn't from the expansion of space, it is result of dynamics that galaxies show.
Fig.2.Hubble's observation of all galaxies receding with Earth in the center
It is assumed that interpretation issues of observation results above applied most in physicists and astronomers introducing expansion of space. When observed from Earth, it is observed that all galaxies recede from Earth and the recession velocity also follow all relations of .
To explain this, if position of the Earth is the center of expansion, namely if position of the Earth is the center of universe, this issue can be simply solved but it can be clearly known that Earth isn't the center of the universe from the observation of the universe until now.
It is because Earth isn't the center of the solar system, but is clear to be just a planet and that the solar system isn't the center of the galactic system either.
Therefore, physicists and astronomers had to find a way to explain this and as this couldn't be explained by dynamics, a new concept that "space expands" was introduced. To explain more specifically, it is assumed that the stereotype that Hubble's observation isn't valid in places where expansion isn't in the center had influence.