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Using Hubble parameter defn to change integration variable from t to a

  1. Feb 19, 2013 #1
    1. The problem statement, all variables and given/known data

    r1 = tt1 1/a(t) dt

    Use the Hubble parameter definition to change from t to a, if a(t) = a and a(t1) = 1

    2. Relevant equations

    Hubble parameter H = a' / a where a' = da/dt

    3. The attempt at a solution

    Start with Hubble parameter definition, and rearrange to find dt

    aH = da/dt

    dt = 1/aH da

    Substitute this in to the original integral to get

    r1 = a1 (1/a) (1/aH) da

    Simplify, because

    (1/aH)(1/a) = 1/(a2H) = 1/(aa') (from Hubble parameter defn)

    So r1 = a1 1/(aa') da

    I'm not sure if this is the right approach, and if it is, how do I integrate this expression with respect to a when it has an a' term in it? I think my effort is all wrong, because it does not help me at all with the second part of the question :(

    Any help much appreciated!
     
  2. jcsd
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