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ps9 - Phys/Astro 228 Extragalactic Astronomy and Cosmology...

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Phys/Astro 228: Extragalactic Astronomy and Cosmology December 1 2006 C.–P. Ma Problem Set 9 Due in class Friday Dec 8 Readings: Ch 6 & 8 of Dodelson 1. Time Evolution of the Baryonic Jeans Mass (a) In the radiation-dominated era, show that the baryonic Jeans mass evolves with the scale factor a as M J ( a ) a α 1 . Find the value for α 1 , and estimate M J (in M ) at matter-radiation equality time using current cosmological parameters. (b) After photon decoupling, show that the baryonic Jeans mass evolves as M J ( a ) a α 2 . Find the value for α 2 , and estimate M J (in M ) right after decoupling. Compare your numbers in (a) and (b) and comment on the implications. 2. Two-Point Correlation Function The two-point correlation function of the density perturbation field, δ ( vectorx ) ρ ( vectorx ) / ¯ ρ 1, is defined as ξ ( r ) = ( δ ( vectorx 1 ) δ ( vectorx 2 ) ) , r = | vectorx 1 vectorx 2 | . (1) The power spectrum of the mass density field is defined as P ( k 1 ) (2 π ) 3 δ D ( vector k 1 vector k 2 ) = (Big δ ( vector k 1 ) δ ( vector
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