Scalefactor calculations for special cases using the Friedmann Equationby karan9 Tags: cosmology, friedmann, radiation, redshift, scale factor 

#1
Mar812, 09:31 PM

P: 3

(i) Obtain the scale factor a(t) and redshift z when the energy density of matter and radiation were equal.
(ii) Next use the a(t) relation for a matteronly universe to estimate the time of matterradiation equality. (iii) Repeat (ii) but using the a(t) relation for a radiationonly universe. Which approximation, (ii) or (iii), is closer to the correct answer? Can someone help me? Thanks!! 



#2
Mar912, 01:58 AM

P: 937

How far have you gotten? You should start by figuring out how dust and radiation energy densities depend on the scale factor. You can find this out using the conservation of energymomentum, and the fact that radiation energymomentum tensor is traceless.
After that you just equate the expressions you got, and integrate Friedmann equations 



#3
Mar912, 02:55 AM

P: 3

Ive understood the concept of how I'm supposed to do it. But, I am confused on how to start the radiation equation. As in what formula do I use to find the scale factor for a radiation dominated universe?




#4
Mar912, 09:18 AM

P: 937

Scalefactor calculations for special cases using the Friedmann Equation 



#5
Mar912, 11:04 AM

PF Gold
P: 184

Just remember that the average energy/photon is proportional to 1/a. I'm guessing that you should assume zero curvature, that the density is always at critical, and that the kinetic energy of the matter can be neglected. You'll need to assume some value for the amount of matter per photon (about 10^{35}kg/photon).




#6
Mar912, 05:23 PM

P: 3

Oh that clears up part i for me. Thanks guys!! My answer for part i comes to a=2.8*10^4
Is that right? I am confused about the method we have been asked to use for part ii. Do i just plug in the value of a into the (da)^2 = Ho^2/a^2 equation and solve for 't' ? Am I missing something? Thanks Again. 



#7
Mar912, 09:07 PM

PF Gold
P: 184

Also remember that the average energy per blackbody photon is ~2.7kT, which is a little higher than you might guess.
Just to give a few clues, with radiation only, you'll find that a [itex]\propto[/itex] t^{1/2} whereas with matter only, a [itex]\propto[/itex] t^{2/3}. Then [itex]\rho[/itex] [itex]\propto[/itex] k/t^{n} where n is a certain positive integer that I won't disclose (same integer for radiation and matter), and k is a constant, although k_{radiation} is slightly larger than k_{matter}. 


Register to reply 
Related Discussions  
Special Cases for Gravity Force Inside Solid Objects  General Physics  1  
Special cases of the Schroedinger Eq?  Quantum Physics  2  
Friedmann Equation  Cosmology  9  
Atwood Machine Special Cases  Introductory Physics Homework  1  
Friedmann equation  Cosmology  3 