From friedmann equa8on h 8 g u u u a 0 2

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Unformatted text preview: gy •  Consider a sphere of radius r, filled with cold par8cles of _______ density ρ (“dust”) 4π M= •  Mass interior to sphere: !! 3 r(t) ρ(t) •  Gravita8onal accelera8on of test mass is: 3 d 2r =− 2 dt !! € •  Mul8ply by dr/dt & integrate over 8me: 2 € 5/21/13 1 ! dr $ GM +k # &= 2 " dt % r (t ) UW, ASTR 323, SP13, Eric Agol ©2013 15 Expansion history k>0 2 k=0 1 ! dr $ GM +k # &= 2 " dt % r (t ) k<0 5/21/13 UW, ASTR 323, SP13, Eric Agol ©2013 16 Newtonian Friedmann equa8on •  Rewrite this in terms of scale factor: r(t)=a(t)r0 2 !...
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This document was uploaded on 04/05/2014.

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