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 .

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 have no idea but I think it has something to do with gravity, I hope you dont waste a bunch of time following this possible dead end though.

Here is one way:

 

You have to help me and do the calculations because I don't have time. I can just tell you steps.

 

take the present CMB temp 2.7 kelvin and raise to fourth use your formula and get ENERGY DENSITY AT PRESENT OF CMB

 

now you want to find the MATTER DENSITY at present but you want it in ENERGY-EQUIVALENT FORM (by the E=mc^2 equivalence).

 

I assume you are in an astronomy class and you know how to get the critical density of the universe assuming flat----the matter density is just 27 percent of that rho-crit.

 

I dont want to do the calculation for you but the matter density is about 0.22 joules per cubic kilometer----express that as joules per cubic meter.

that includes dark matter. check my arithmetic.

 

so now you have two energy densities. joules per cubic meter of CMB and joules per cubic meter of matter.

 

THE REDSHIFT Z AT WHICH THEY WERE EQUAL IS SIMPLY THEIR RATIO.

 

 

so it is really a trivial calculation, I think the answer comes out around z = 3000 but that is a wild guess and you have to do the calculation.

 

the reason for this is that the energy in the CMB totally way dominates the energy in all other kind radiation

so you just have to work back to the redshift z where CMB density equals matter density

thanks, but we're assuming no dark matter in the universe, what would the answer be then