Examining Matter Dominance in FRW Universe: Solution

[bon]

Homework Statement

Metric: ds^2 = -c^2 dt^2 + (t/t*) (dx^2 + dy^2 + dz^2)

(I guess t* is a constant?)

Is this universe matter dominant? Explain

Homework Equations

The Attempt at a Solution

I guess you have to use the FRW equation?

Assuming the usual FRW form, we set a^2 = t/t*

to find H^2 depends on 1/a^4. This means it's radiation dominant, right?

Thanks

 

[Clever-Name]

If H^2 depends on 1/a^4 then yes, this is radiation dominant since matter is a^-3 dependent. I didn't check the work though.