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, t0 , in terms of the Hubble and the density parameters. (a) For Ω Λ = 0 models, plot t0 in units of h-1 Gyr versus the matter density parameter Ω0 ,m , for0 ≤ Ω0 ,m ≤ 2 . 5. What is the general trend of t0 as the matter density increases? (b) On the same plot, add a curve for t0 vs. Ω0 ,m for ±at models (i.e. Ω0 ,m + Ω0 , Λ = 1). (c) Consider the ±at models in (b). Plot H0 , in units of km s-1 Mpc-1 , versus Ω0 ,m (same range as (b)), for 3 values of t0 : 11.5, 13.7, 18 Gyr. Current observations ²nd H0 ≈ 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 Ω0 ,m implied by your curves? For some years, Ω
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This note was uploaded on 08/01/2008 for the course ASTRO 228 taught by Professor Chungpeima during the Fall '06 term at University of California, Berkeley.