1. The problem statement, all variables and given/known data 1) Calculate the angular diameter distance to the last scattering surface in the following cosmological models: i) Open universe, ΩΛ= 0.65, Ωm = 0.30 ii) Closed universe, ΩΛ = 0.75, Ωm = 0.30 ii) Flat universe, ΩΛ = 0.75, Ωm = 0.25 Describe how the CMB power spectrum changes in each of these models. Compare your results to the Benchmark model, ΩΛ = 0.7, Ωm = 0.3 2. Relevant equations dA=dhor(t0)/zls dhor(t0)= c ∫ dt\a(t) H2/H02 = Ωr/a4+Ωm/a3+(1-Ωr-Ωm-ΩΛ)/a2+ΩΛ H0t=∫1als da[Ωr/a^2+Ωm/a + ΩΛa2+(1-Ωr-Ωm-ΩΛ)]-1/2 zls=1100 als= 1/(1+zls) 3. The attempt at a solution First off, is is it safe to assume that Hot is the horizon distance (or proper distance)? Because that's what I'm going off of so if that's not correct then everything I've done is wrong anyway. So far I have tried doing the integration of the 4th equation listed above for the open universe but I keep getting a negative number. Does the negative just mean that its in the past time? And if my assumption that Ht is not the horizon distance, then how do I relate the answer from the integral to the equation for the horizon distance (the 2nd eq listed above)? I think that the integration I did (eq 4) gives me t(a) rather than a(t) but then do I need to get a(t) in order to do the integral for dhor? Sorry if my questions are confusing. I am lost in a sea of equations and integrations.