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Midterm 2013

In this problem you will prove this relation a use the

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Unformatted text preview: iverse that contains only matter (negligible Λ or radiation) and is slightly open or closed (“slightly” meaning |Ωk|<<1) satisfies 2/3 Ⱥ 1 Ⱥ 3 ȹ t ȹ Ⱥ1 − Ωk ȹ ȹ + O(Ω2 ) Ⱥ . (1) ρm = k 6πGt 2 Ⱥ 5 ȹ t 0 Ⱥ Ⱥ Ⱥ Ⱥ (This is a Taylor expansion in Ωk.) In class, Equation (1) was used in the analysis of large scale perturbations in the Universe. In this problem you will prove this relation. € (a) Use the Friedmann equation to show tha...
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