1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook