One point accelerated expansion model, the Universe

[alpha2cen]

This is one point constant accelerated expansion model.

Observer line calculation
t_current=t+L/C
t_current=t+(L_initial +vt)/C
v=(Ct_current-L_initial)(1/t) -C
t_current; current time, 13.75billion year
L_initial; initial Supercluster distance from the Earth

 

In the case of constant acceleration

Observer line calculation
t_current =t+L/C
t_current=t+(L_initial +(1/2)vt)/C
where (1/2)v is average velocity value from Big Bang to a point.
Solve above equation to the v.
v=(2C t_current -2L_initial)(1/t) -2C
one point expansion, Linitial=0
v=(2C t_current )(1/t) -2C
v; speed of expansion(1x10²²km/billion year)
C; speed of light(9.46x10²¹km/billion year)
t; time(billion year)
t_current; current time(13.75 billion year)

 

Speed line calculation
We do not know Supercluster’s moving speed 1 billion light years away.
So we use the light which begins 1billion years ago and arrives at present.
v=(2C t_current )(1/t) -2C

t1=12.75 billion yr, v=v1
From the obtained (t1, v1) value we calculate gradient a
a1=v1/t1
For calculation we think about the Universe model.
The model is like this.
At the big bang, every Super cluster attached at the one point.
——–000000———-
Some billion years later
—-0—0—0—0—0—0—..
At the present
—–0——–0——–0——–0—..
So, near first 1 billion away Super cluster's moving speed is
v1=a1t
2billion away Super cluster's moving speed
v2=2a1t
4billion away Super cluster's moving speed
v4=4a1t
8billion away Super cluster's moving speed
v8=8a1t
16 billion away Super cluster's moving speed
v16=16a1t

Edited December 10, 2012 by alpha2cen

[Spyman]

First I would like to point out that in the mainstream view the expansion of the Universe does not have constant acceleration. The expansion had a very high rate at the time of the Big Bang and then slowed down due to gravity for around the first half of its age and then started to accelerate in the last half of its lifetime. The Hubble constant is thus only constant over space and varies during time.

 

We can still discuss an hypothetical universe that has an expansion with constant acceleration. But if the expansion is scalar like in the theory of Relativity there is a very important difference from objects accelerating away from each other through space instead of space expanding between them.

 

Imagine that you have a rubber band and a small wheel, it takes 10 turns of the wheel to travel from one side of the band to the other when it is relaxed and 20 turns when it is expanded, but if the band is streching from relaxed to expanded state during the time while the wheel is rotating from one side to the other, then the wheel rotations will measure a third distance which is how long distance it had to travel along the band from one end to the other.

 

Likewise if a photon was emitted from a distance of about 4 billion lightyears and that galaxy is now around 26 billion lightyears distant due to expansion, but it took 12 billion years for the photon to reach us, so the photon only propagated 12 billion lightyears through space, because the photon didn't wait until the expansion had finished but moved simultaneously during the expansion and covered distances before it had fully expanded.

 

If space was not expanding and the galaxy was instead accelerating away from us through space then it would only take 4 billion years for the photon to reach us from an emitting distance of 4 billion lightyears apart, independent of the speed and acceleration of the observed galaxy itself.

A constant acceleration of the expansion also has a border where the rate of expansion is faster than the speed of light, there will be a shrinking event horizon preventing photons from objects beyond this distance to forever be unable to reach us. Together with the age limit of the Universe that creates a growing border allowing light from greater distances to reach us as time passes, we will be severely limited in how far we can observe.