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Astrophysics homework: Cosmology

  1. Jun 3, 2008 #1
    [SOLVED] Astrophysics homework: Cosmology

    1. The problem statement, all variables and given/known data
    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]

    3. 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.
  2. jcsd
  3. Jun 3, 2008 #2
    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.
  4. Jun 4, 2008 #3
    That's right, I forgot that. I worked it out now - it really is straight-forward.

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