1 da 8 gut c 2 22 2 3c a rc 0 3 a dt where

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Unformatted text preview: ls out, leaving the Friedmann equa8on: 2 ! 1 da $ 8π Gρ 2k +22 # &= 3 r0 a " a dt % 5/23/13 UW, ASTR 323, SP13, Eric Agol ©2013 4 Rela8vis8c Friedmann equa8on •  Describes the evolu8on of the scale factor with 8me: 2 ! 1 da $ 8π Gu(t ) κ c 2 Λ − 22 + # &= 2 3c a rc ,0 3 " a dt % •  where u(t) is the total _______ density of maZer and radia8on (baryons, dark- maZer, photons, neutrinos) in units of _________ •  Λ is the cosmological constant. If uΛ=Λc2/(8πG), then 2 H= 5/23/13 8π G(ur + um + uΛ ) 3c 2 2 κc − 22 a rc ,0 UW, ASTR 323, SP13, Eric Agol ©2013 5 Cri8cal density •  This is the energy density of the Universe such that the Universe geometry is flat (we think we live in such a Universe): κ=0 •  A flat Universe is always _____. From Friedmann equa8on: #H − 8π G (u + u + u )&a = 0 % ( 2 $ •  Implies: •  Currently: 5/23/13 2 3c 2 r m Λ ' 3H 2c 2 ur + um + uΛ = ≡ ρC c 2 8π G 2 3H0 ρC ,0 = = 8πG...
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This document was uploaded on 04/05/2014.

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