r dt at distance traveled by light beam a is ct

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: r ,0 = H0 % + + ΩΛ ,0 % dt $ & ( ( ' •  Given H0, Ωm,0, Ωr,0 & ΩΛ , this can be integrated backwards w.r.t. 8me to find t(a). 5/23/13 UW, ASTR 323, SP13, Eric Agol ©2013 14 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 maZer, w=0, so a∝ 5/23/13 UW, ASTR 323, SP13, Eric Agol ©2013 15 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 5/23/13 UW, ASTR 323, SP13, Eric Agol ©2013 16 Time versus redshiS •  The lookback 8me is 8me that has passed since light was emiZed at a par8cular redshiS •  Compute from the metric: z = 1 / a − 1,$so dz / dt = −H / a = −H(1 + z),$so dz dt = − H(1 + z) •  Thus the lookback 8me is: t0 ∫ dt = te 5/23/13 z ∫ 0 dz" 1 ≈ H(z")(1 + z&...
View Full Document

Ask a homework question - tutors are online