# Distance to surface of last scattering in +, -, and flat uni's

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1. Mar 27, 2016

### thecourtholio

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 ∫tet0 dt\a(t)
H2/H02 = Ωm/a2+(1-ΩmΛ)/a2Λ
H0t=∫0a da[Ωm/a + ΩΛa2+(1-ΩmΛ)]-1/2
zls=1100

3. The attempt at a solution
Honestly, I'm not even sure where to start. My main problem is with part 1 and 2 for the open and closed universes and trying to calculate the horizon distances in those universes. I think I'm just having problems understanding how to relate the friedmann equation (the third one listed above) to the horizon distance (the second equation). In my textbook it says that for the benchmark model dhor(t0) = 3.24c/H0 but where did they get the 3.24?
If someone could just kind of point me to the right direction that would be super appreciated. Also, my integral skills are a little rusty so any help with those would be awesome.

2. Apr 1, 2016