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Unformatted text preview: Phys/Astro 228: Extragalactic Astronomy and Cosmology November 3 2006 C.–P. Ma Problem Set 7 Due in class Friday November 17 Reading: Chapter 7 of Dodelson 1. Structure Formation I: Radiation Era In class we derived the time evolution of density perturbation in nonrelativistic matter δ m (above the Jeans length) in the matterdominated era. Here we will find the behavior of δ m in the radiation dominated era. Assume a flat, Ω Λ = 0 universe for simplicity. (a) Assume that the perturbation in radiation, δ r , is negligible. Show that the linearized evolution equation for δ m can be written as d 2 δ m dy 2 + 2 + 3 y 2 y (1 + y ) dδ m dy − 3 2 y (1 + y ) δ m = 0 , (1) where y ≡ ρ m /ρ r = a/a eq and a eq is the equality time. (b) At late time ( y ≫ 1), compare your solutions for δ m with those derived in class. (c) Verify that δ m ∝ y + 2 / 3 is a solution to eq. (1) in general. Can δ m grow much in the radiation dominated era?...
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 Fall '06
 CHUNGPEIMA
 Cosmology, Dark Matter, Extragalactic Astronomy and Cosmology, density perturbation, Structure Formation

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