1. The problem statement, all variables and given/known data Our universe is observed to be flat, with density parameters Ωm,0 = 0.3 in non-relativistic matter and Ω[itex]\Lambda[/itex],0 = 0.7 in dark energy at the present time. Neglect the contribution from relativistic matter. At what redshift did the expansion of the universe start to change from deceleration from acceleration? 2. Relevant equations a(t=change) = 0 a(t=now) = 1 (? is this convention?) ((da/dt) * (1/a))2 = H02 E2(z) where E2(z) = Ω[itex]\Lambda[/itex],0 + (1-Ω0)(1+z)2 + Ωm,0(1+z)3 z = a0/a(t) -1 where a0 denotes the present time 3. The attempt at a solution First I thought about setting (da/dt)*(1/a) equal to zero and solving the equation for z. However, this gives a redshift of -2.32 which doesn't really make sense as the negative value implies that there is a blueshift (right?) Upon further thought, I realized that a = 0 means that the lefthand side of the equation should be undefined / go to infinity... so could z be infinity? This doesn't really make sense to me either but it's all I've got. I can manipulate the other equation I found to also give z=infinity by setting a(t) equal to zero. I'm sure I'm forgetting some important concept but that's what I've got so far.