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# ps3 - Phys/Astro 228 Extragalactic Astronomy and Cosmology...

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Phys/Astro 228: Extragalactic Astronomy and Cosmology September 22 2006 C.–P. Ma Problem Set 3 Due in class Friday September 29 Readings: Chapter 2 of Dodelson and Sec 19.2 of “Big Bang Cosmology” from Review of Particle Physics (see link at course website). 1. Age of the Universe In class, we derived expressions for the age of the universe, t 0 , in terms of the Hubble and the density parameters. (a) For Ω Λ = 0 models, plot t 0 in units of h - 1 Gyr versus the matter density parameter Ω 0 ,m , for 0 Ω 0 ,m 2 . 5. What is the general trend of t 0 as the matter density increases? (b) On the same plot, add a curve for t 0 vs. Ω 0 ,m for flat models (i.e. Ω 0 ,m + Ω 0 , Λ = 1). (c) Consider the flat models in (b). Plot H 0 , in units of km s - 1 Mpc - 1 , versus Ω 0 ,m (same range as (b)), for 3 values of t 0 : 11.5, 13.7, 18 Gyr. Current observations find H 0 72 km s - 1 Mpc - 1 , and the oldest objects in the universe is at least 11.5 Gyr old. Given these, what is the constraint on Ω 0 ,m implied by your curves?
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