Phys/Astro 228: Extragalactic Astronomy and CosmologySeptember 22 2006C.–P. MaProblem Set 3Due in class Friday September 29Readings: Chapter 2 of Dodelson and Sec 19.2 of “Big Bang Cosmology” from Reviewof Particle Physics (see link at course website).1.Age of the UniverseIn class, we derived expressions for the age of the universe,t0, in terms of the Hubble and the densityparameters.(a) For ΩΛ= 0 models, plott0in units ofh-1Gyr versus the matter density parameter Ω0,m, for0≤Ω0,m≤2.5. What is the general trend oft0as the matter density increases?(b) On the same plot, add a curve fort0vs. Ω0,mfor flat models (i.e. Ω0,m+ Ω0,Λ= 1).(c) Consider the flat models in (b). PlotH0, in units of km s-1Mpc-1, versus Ω0,m(same range as(b)), for 3 values oft0: 11.5, 13.7, 18 Gyr. Current observations findH0≈72 km s-1Mpc-1, andthe oldest objects in the universe isat least11.5 Gyr old. Given these, what is the constraint on Ω0,mimplied by your curves?
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