Calculating Age of Universe Using Redshift: 0.6

[b_o3]

Hi i am confused as to how to calculate the age of the universe with redshift
say for example

The age of the universe now is 13.4 billion years old (and a critical universe).
How do i find the age of the universe if it was a redshift at say 0.6??

Do i have to find the scale factor first?
I am not very sure, please help!

 

[Dick]

You need to know the ratio of the scale factors. z=(a0/a)-1 where a is the scale factor then and a0 is the scale factor now.

 

[b_o3]

how do i get that? do i have to integrate first

 

[Dick]

No. To a good approximation the universe has been matter dominated all of it's history. What does a(t) look like as a function of t in this case?

 

[b_o3]

so how would that work then?

 

[Dick]

What does a(t) look like as a function of t in a matter dominated universe? You can look it up, it's a power law.

 

[b_o3]

to the power of 4

 

[Dick]

Nope. Use the Friedmann equation. H^2 is proportional to rho. If a(t)=t^n. H is proportional to 1/t. rho is proportional to 1/a(t)^3. So 1/t^2 is proportional to 1/a(t)^3. So a(t) is proportional to t^(2/3).

 

[b_o3]

I'm sorry I'm not an expert on this I don't usually take science courses... but are u saying I'm gna take a(t)= k * t^(2/3) . and that gives me the answer?

 

[Dick]

Yes. Since z=(a0/a)-1, this gives z=(t0/t)^(2/3)-1. (t0 is the age of the universe and t is time at redshift z. It's an approximation but it should do. You are asking some pretty hard questions for a non-science course person. What's the course?