Calculating the redshift at which radiation energy density equaled mass density

[yijiao]

how do you calculate the redshift at which the universe shifted from radiation dominated to mass dominated

i was told to assume a flat universe with H0 = 70

also the temperature, to which i was given the formula density rad = aT^4

for the first part, i tried using density is propotional to scale factor ^3 and ^4

but it's not working too hot :(

help please, i need it done by tonight :(

 

[marcus]

how do you calculate the redshift at which the universe shifted from radiation dominated to mass dominated

i was told to assume a flat universe with H0 = 70

also the temperature, to which i was given the formula density rad = aT^4

for the first part, i tried using density is propotional to scale factor ^3 and ^4

but it's not working too hot :(

help please, i need it done by tonight :(

Gee you have to get it done by tonight. There are some other guys who are really good, but they are not around right now. I will try to help a little in case they don't show up before you have to finish.

I think the answer is z= 3200, or so.

You know that for the CMB the redshift is z = 1100, so this is longer ago than the recombination.

I guess you take the energy density of the CMB, and multiply by 3200⁴
and you take the energy-equivalent of matter density and multiply by 3200³

and the two energy densities are supposed to be equal at the transition

I think there is a lot of cancelation, and that what it comes down to is this equation

3200 x CMB energy density = matter energy density

And what that boils down to is an equation for z (which I suspect is around 3200). Here is the equation

z = (CMB energy density)/(equivalent energy density of matter)
============

if 3200 is the right z, then the temperature at the time would have been

3200 x 2.725 kelvin.

Im answering quick without really remembering the material but if you need quick help you can try to get some good out of this. Dont rely on it or trust it too much tho. Good luck

 

[Chronos]

If it's of any use, the gruesome details can be found here:
http://www.astro.uu.se/~nisse/courses/kos2006/lnotes/ln6.pdf

 

[marcus]

If it's of any use, the gruesome details can be found here:
http://www.astro.uu.se/~nisse/courses/kos2006/lnotes/ln6.pdf

that does indeed have it
equations 134 thru 137 on page 3 (so you won't have to hunt thru the whole thing), and the answer they get is approximately z = 3600

this is the redshift for "matter-radiation equality"

the redshift for "recombination" (origin of CMB) is about z = 1100 and they also derive an estimate of that.

good find! some Swedish professor's course material apparently. could be useful for other things as well.

(there is a subtlety---this guy includes NEUTRINOS as radiation because back in those days they would be so hot they would be relativistic. so he treats the neutrino background as radiation, and that is what leads him to say 3600. If he didnt he'd get a higher estimate for z---so that was a flaw in my quick sloppy response a few days ago)

 

[Chronos]

Your post was not flawed, it was rigorously correct. Using the neutrino correction is speculative. Your z~3200 result is within the error bars and well reasoned. Your cold, logical explanations are simply amazing.