redshift

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 Boltzman 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 dont 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 im 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 gonna 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