hw11 - Physics 3002, Problem Set 11, due 4/29/09 Lam Hui 1....

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Unformatted text preview: Physics 3002, Problem Set 11, due 4/29/09 Lam Hui 1. This is based on Ryden problem 9.4. Find the luminosity distance d L to the surface of last scattering. You can assume the redshift of the last scattering surface is z = 1100. First, write down an exact expression for d L for the Benchmark Model (i.e. a flat universe with m, = 0 . 3 and , = 0 . 7). The exact expression would involve an integral that is hard to do. Dont bother doing it. Second, lets approximate the integral by putting m, = 1 and , = 0. This time, you should be able to do the integral and find d L in Mpc (assuming H = 70 km/s/Mpc). 2. In class, we introduced the idea of optical depth which gives us the prob- ability that a photon is scattered as it travels through a gas of electrons. We wrote it as = integraldisplay dlscript 1 / ( n e e ) (1) where n e is the (proper) number density of electrons, e is the Compton scat- tering cross-section, and dlscript is an infinitesimal (proper) distance that the photon...
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This note was uploaded on 02/23/2010 for the course PHYS 3002 taught by Professor Lam during the Spring '10 term at Columbia.

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