Rt 8me to nd ta 52313 uw astr 323 sp13 eric agol

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Unformatted text preview: , SP13, Eric Agol ©2013 The Planck Collabora8on: Ade et al. (2013) 11 Equa8on of state •  The rate of expansion of the Universe needs to take into account the fact that the ______ _______ of fluid changes with 8me d (a3 ρ ) P da3 •  The first law of thermodynamics gives: =− 2 dt c dt •  The general equa8on of state for a fluid can be wriZen as: P !! = •  Where w≈0 for maZer (P<<ρc2), w=1/3 for radia8on, and w=? for the cosmological constant (HW) 5/23/13 € UW, ASTR 323, SP13, Eric Agol ©2013 12 Energy density vs. scale factor 20 ur∝ a-4 15 log(u) 10 5 um∝ a-3 0 uΛ∝ a0 -5 -10 -6 5/23/13 -4 -2 log(a) UW, ASTR 323, SP13, Eric Agol ©2013 0 2 13 Expansion History •  The accelera8on of the Universe can be derived from the Friedmann equa8on: $Ω ' Ω H= + +Ω ) & & ) % ( !! •  This can be rewriZen as: 1 /2 2 € r ,0 m ,0 Λ ,0 #Ω Ωm ,0 da...
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