1. The problem statement, all variables and given/known data r1 = t∫t1 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 = a∫1 (1/a) (1/aH) da Simplify, because (1/aH)(1/a) = 1/(a2H) = 1/(aa') (from Hubble parameter defn) So r1 = a∫1 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!