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# A13w 2 0 2a3 3 2 h012t 0 for radia8on

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Unformatted text preview: egrated backwards w.r.t. 8me to ﬁnd t(a). 5/28/13 UW, ASTR 323, SP13, Eric Agol ©2013 4 Expansion rate •  In a ﬂat Universe where one component dominates, da 1/2 − (1+3w )/2 dt = H0Ω0 a •  Integra8ng this (for w≠- 1) gives: a da!a!(1+3w )/2 = ∫ 0 2a3( 3( )/2 ) = H0Ω1/2t 0 •  For radia8on, w=1/3, so a∝ •  For cold maRer, w=0, so a∝ 5/28/13 UW, ASTR 323, SP13, Eric Agol ©2013 5 Expansion History 102 ΩΛ=0.685 101 a∝eHt 100 Ωm,0=0.315 a(t) 10-1 a(t)= 10 (1+z)- 1 10 a∝t2/3 -2 -3 a∝t1/2 10-4 Ωr,0=4.6e-5 10-5 10-8 10-6 10-4 10-2 100 102 H 0t 5/28/13 UW, ASTR 323, SP13, Eric Agol ©2013 6 Proper distance •  r(t)=a(t)r0 - instantaneous separa8on – _________ to measure! •  What we can measure is the trajectory of light for which dl =___ (‘null geodesic’). In a ﬂat Unive...
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