(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the angular size of the comoving horizon at the z=1100 last scattering surface, as projected on to the current (CMB) sky. Assume flat FRW cosmology and no cosmological constant. First calculate angular diameter distance to last scattering, then the particle horizon at last scattering.

2. Relevant equations

Particle horizon d_{H}= a(t) ∫_{0}^{t}dt'/at' = a(η)η

Angular diameter distance d_{A}= R_{0}S_{k}(χ)/(1 + z) = d_{L}/(1+z)^{2}

3. The attempt at a solution

I have used a = 1/(1+z) to go from z = 1100 to a = 9.08 x 10^{-4}

Looking at the definition of particle horizon, I need to find what t is at z = 1100, so I tried to get this using the first Friedman equation, and rearranging it to get

da/dt = a √(8∏Gρ/3)

1/a da = √(8∏Gρ/3) dt

∫ 1/a da = √(8∏G/3) ∫ρ(t) dt

I don't know how to go any further with this though to find t at some a.

Looking at the angular diameter distance, I have a flat unverse, so S_{k}(χ) = χ. I think R_{0}and χ are both just arbitrary measures though, so I have no idea how to do anything useful with that definition!

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# Homework Help: Angular size of comoving horizon at last scattering

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