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Calculating the redshift at which radiation energy density equaled mass density 
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#1
Apr307, 04:26 PM

P: 1

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 :( 


#2
Apr307, 05:01 PM

Astronomy
Sci Advisor
PF Gold
P: 23,228

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 3200^{4} and you take the energyequivalent of matter density and multiply by 3200^{3} 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 


#3
Apr707, 07:00 AM

Sci Advisor
PF Gold
P: 9,446

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


#4
Apr707, 08:04 AM

Astronomy
Sci Advisor
PF Gold
P: 23,228

Calculating the redshift at which radiation energy density equaled mass density
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 "matterradiation 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 subtletythis 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 zso that was a flaw in my quick sloppy response a few days ago) 


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