# I Redshift and Scale factor

1. Dec 31, 2017

### Arman777

We can define the relationship between $z$ and $a(t_e)$ as,

$$1+z=\frac {a(t_0)=1} {a(t_e)}$$

When we assume $z=2$, it means that $a(t_e)=\frac {1} {3}$

Is this means that universe was $\frac {1} {3}$ times smaller then now ?

If its the case then lets suppose $z=6$ which means universe was $\frac {1} {7}$ times smaller, but even in this case it doesnt seem a huge difference between $z=2$ and $z=6$. But I think there should be a lot of difference.

I am not sure what am I missing.

Thanks

2. Dec 31, 2017

### Orodruin

Staff Emeritus
Why?

3. Dec 31, 2017

### Arman777

The largest value of z can be 10 and it that case universe was 1 billion years old maybe more young like a 500 million years old. I am not sure but in any case.

Lets suppose $z=10$, in that time lets suppose radius of OU is $r$ and now its $11r$?
Cause I was espanding like $10^10$ difference cause universe was so young those times.

For a current scale of the OU is 45 billion light year. 11 times smaller means 4 billion light year. But I was expanding like a million light year or maybe less If I think the time scale which it grow 11 times bigger in 13 billion years ?

I am not sure how can I explain it.

4. Dec 31, 2017

### Bandersnatch

The CMBR is z = 1089. There is no upper limit for z.

5. Dec 31, 2017

### Orodruin

Staff Emeritus
Why do you think that z cannot be larger than 10? It is false. The redshift at the last scattering surface is about 1000.

6. Dec 31, 2017

### Arman777

7. Dec 31, 2017

### Bandersnatch

8. Dec 31, 2017

### Orodruin

Staff Emeritus
They are studying galaxies. It took some time for galaxies to evolve and you will not find galaxies with a redshift of z = 1000. This does not mean that redshifts larger than 10 does not exist.

9. Dec 31, 2017

### Arman777

Thanks for your replies. I understand it now