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Astrophysics homework: Cosmology

  • Thread starter Niles
  • Start date
  • #1
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[SOLVED] Astrophysics homework: Cosmology

Homework Statement


I have to show that during the Big Bang Nuchleosynthesis, the scalefactor is approximately given by

[tex]a(t) = \left( {4H_0^2 \Omega _{r,0} } \right)^{1/4} \sqrt t [/tex]

The Attempt at a Solution


Ok, since the BBNS is during the first ~3 minutes after Big Bang, we are in a flat radiation-dominated Universe. The Friedmann equation takes the form:

[tex]\frac{{H^2 }}{{H_0^2 }} = \frac{{\Omega _{r,0} }}{{a^4 }}[/tex]

I rewrite and integrate this and I get that

[tex]a(t) = \left( {3tH_0 \sqrt {\Omega _{r,0} } } \right)^{1/3} [/tex]

Can you guys find my error? This problem seems quite straight-forward, but I can't find my error.
 

Answers and Replies

  • #2
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I think you forgot this:

[tex] H = \frac{{1}}{{a}} \frac{{da}}{{dt}} [/tex]

or else you lost track of another one of the a's during your integration.
 
  • #3
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That's right, I forgot that. I worked it out now - it really is straight-forward.

Thanks.
 

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