1. Main Text
We use the following equations:
Distance Modulus
where (m − M) is the observed magnitude in Figure 1, and Δd is the difference between two consecutive values (m − M) for z.
Radial Velocity
where z is the Redshift and
where x is the next higher value of z.
Average Velocity
.
.
Average Acceleration
.
From Figure 1 and the equation for distance (d), we get the following values for Table 1.
From the equation for radial velocity, we get the following values for Tables 2-4.
Two first dimensions form half of the second dimension that join with a Big Bang to complete the second dimension.
Three second dimensions form one-third of the third dimension that join with a Big Bang to complete the third dimension.
Four third dimensions (of which we are one) form one-fourth of the fourth dimension that join with a Big Bang to complete the fourth dimension.
n, (n − 1) dimensions form one-nth of the nth dimension that join with a Big Bang to complete the nth dimension [1] .
Table 2. Redshift vs Radial Velocity.
Table 4. Total Values for plotting Figures 2-4.
Figure 1. The accelerated expansion of the Universe [2] [3] .
Figure 3. Velocity(av.)-time graph No. 2.
Figure 4. Acceleration(av.)-time graph No. 3.
2. Conclusion
From the Distance-Time Graph we see that space is expanding exponentially while its acceleration continues to increase. The spatial exponential expansion of the lower dimensions halts as several of the lower dimensions join with a Big Bang to form the next higher exponentially increasing spatial dimension with the lower dimensions forming the surface area of the higher dimension. This process continues until the final level of the Multiverse has been reached.