Calculating the Transition from Radiation to Matter Dominated Universe

[b_o3]

Hi, I really need help with this question I've tried everything!

let's assume a critical/flat universe. Ho=70 km/s/Mpc. I computed Boltzmann law for energy (volume) density by integrating Planck's law p rad= alpha*T^4. alpha= 7.56*10^-15 ergs/cm^3/K^4 (Which I computed to be 7.56*10^-16 Joules/m^3/K^4)

I don't know where to begin with this question.. there's no other values provided . I'm supposed to somehow find out the redshift at which the universe switched from being radiation dominated to matter dominated (point of time at which radiation density is equal to mass density). and the temperature of the universe at that time .

I tried making a formula by putting radiation density formula= matter density formula ,, but there's not enough values given to compute it.

thanks!

 

[Dick]

You can ignore the current energy density of radiation compared with matter. Which means you can use the value of Ho to determine the matter energy density via the first Friedmann equation. Ignore the curvature term as well.

 

[b_o3]

so do I have all the values i need?

 

[Dick]

You tell me. What is current mass and radiation density and how do they scale with the expansion?

 

[b_o3]

sorry but I am not following

 

[Dick]

How would you use Ho to determine the current sum of radiation and mass density? Hint: I already told you.

 

[b_o3]

okay so after i do that... hows that going to help

 

[Dick]

Then use the fact that radiation scales as 1/a(t)^4 and matter scales as 1/a(t)^3. If you know their current values you can find out the scale factor where they are equal.

 

[b_o3]

cant i just equate 1/a(t)^4=1/a(t)^3 . then I would get the value of a(t) when they are equal