ps4 - Phys/Astro 228 Extragalactic Astronomy and Cosmology...

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Phys/Astro 228: Extragalactic Astronomy and Cosmology September 29 2006 C.–P. Ma Problem Set 4 Due 5pm Friday October 6 in grader Brad Hagan’s mailbox, Campbell Hall 6th floor mailroom. Readings: (1) Ch 3 of Dodelson; (2) Sec 19.3 of “Big-Bang Cosmology” (Note that they set c = h = k B = 1 and didn’t know 90 32 is 45 16 .) (3) All of “Big-Bang Nucleosynthesis” (linked at course website). 1. Ω in Photon Background Radiation The present temperature of the cosmic background photons is known to exquisite precision: T 0 = 2 . 725 ± 0 . 001(1 σ ) Kelvin (Mather et al 1999). (a) Calculate the present number density of photons (in cm - 3 ) in this radiation. (Don’t worry about the error bars.) (b) Calculate Ω 0 , the present ratio of the mass-energy density in photons to the critical density. (Express your answer in terms of the Hubble parameter h .) Is the universe today radiation or matter dominated? 2. Ω in Neutrino Background Radiation (a) From the photon temperature above, calculate the present temperature of the neutrino background T 0 .
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