1. The problem statement, all variables and given/known data Integrate field equations for a universe filled with radiation and with k = +1, λ = 0. Find ρ(a) ρ(t) and a(t). Find lifetime of the universe. 2. Relevant equations Use first Friedmann equation which reduces to a'2/a2 + a-2 = kρ where k = 8∏/3 3. The attempt at a solution I have followed my lecture notes to get the following expression for a(t) a(t) = (k - t2)1/2 In radiation domination we have ρ(a) = ρ0a-4 which leads to ρ(t) = ρ0(k - t2)-2 Hopefully these results are correct! I am not sure how to o the last part though, which is to calculate the lifetime of the universe. Can someone advise where to start with this? Presumably I want t as a function of . . . something. And with a closed universe I think the lifetime ends when a reaches 0 again (the big crunch). But I'm not sure where to go from there . . .