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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 non-relativistic matter m (above the Jeans length) in the matter-dominated era. Here we will find the behavior of m in the radiation- dominated era. Assume a flat, = 0 universe for simplicity. (a) Assume that the perturbation in radiation, r , is negligible. Show that the linearized evolution equation for m can be written as d 2 m dy 2 + 2 + 3 y 2 y (1 + y ) d m dy 3 2 y (1 + y ) m = 0 , (1) where y m / r = a/a eq and a eq is the equality time. (b) At late time ( y 1), compare your solutions for m with those derived in class. (c) Verify that m y + 2 / 3 is a solution to eq. (1) in general. Can m grow much in the radiation- dominated era?...
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- Fall '06