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At what redshift does energy density in matter equal energy density in radiation? 
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#1
Mar1510, 02:56 PM

P: 467

Hello. This is question for my course work, I was wondering if I could get some insight, here is the question:
Assume that the vast majority of the photons in the present Universe are cosmic microwave radiation photons that are a relic of the big bang. For simplicity, also assume that all the photons have the energy corresponding to the wavelength of the peak of a 2.73K blackbody radiation curve. At Approximately what redshift will the energy density in radiation be equal to the energy density in matter? (hint: work out the energy density in photons at the present time. Then work it out for baryons, assuming a proton for a typical baryon. Remember how the two quantities scale with redshift to work out when the energy density is the same.) [tex] \rho_M \propto a^{3} [/tex] [tex] \rho_\gamma \propto a^{4} [/tex] [tex] T \propto a^{1} [/tex] [tex] 1 + z = \frac{v}{v_0} = \frac{\lambda_0}{\lambda} = \frac{a(t_0)}{a(t)} [/tex] How can I calculate the energy density of photons and protons at the present time? Do I use E = mc^2? 


#2
Mar1510, 04:51 PM

Sci Advisor
P: 1,253

You need to first consider how to calculate the energy density in radiation, given that you are told that it follows a blackbody spectrum of a given temperature. That's the hardest part of this question. You shouldn't need to worry about the energy of a proton, if you assume a reasonable Hubble's constant value of
[tex]H_0[/tex] ~ [tex]72 Mpc/Km/s [/tex] and a matter density today of [tex] \Omega_m [/tex] ~ [tex]0.3 [/tex] that will give you the matter density today to compare with the radiation density today, then you need to scale these back as function of a the scale factor [tex]a(t)[/tex] to find the point at which they are equal. Then convert that scale factor to a redshift. 


#3
Mar1510, 05:05 PM

P: 467

Do I use the StefanBoltzmann law to calculate radiation density?
How do I use Hubble's constant to solve this? What unit is that matter density measured in? 


#4
Mar1510, 05:16 PM

Sci Advisor
P: 1,253

At what redshift does energy density in matter equal energy density in radiation?



#5
Mar1710, 01:34 AM

P: 1

I'm confused about this same question, can anyone else clarify please?
For energy density of radiation, how would i use the stefan boltzman law? 


#6
Mar1710, 05:20 AM

Sci Advisor
P: 1,253

Write down the Stefan Boltzmann law. Think about the terms in the equation. Which one do you need to calculate, and which ones are you already given?
Note that because this is a homework question, I'm following the guidelines for answering homework from the Homework Help forum, rather than just stating the answer. 


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