probset5a - COSMOLOGY Problem Set 5 April 26, 2010 Problem...

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COSMOLOGY Problem Set 5 April 26, 2010 Problem 1 : ΛCDM Consider the standard ΛCDM cosmological model with Ω M = 0 . 25 and Ω Λ = 0 . 75; you may adopt H 0 = 70 kms - 1 Mpc - 1 . Assume that the current density in relativistic particles (“radiation”) is Ω R = 8 . 0 × 10 - 5 . a) Find the redshift of equal matter and radiation densities, z eq . [5] b) Find the age of the Universe, t eq , at z eq . [5] c) “Recombination” occurs for z rec = 1100. Find the age of the Universe, t rec , at z rec . [5] d) Find the proper radial distance to the horizon at recombination, R H ( t rec ), in units of the present Hubble distance c/H 0 . [10] e) Identify each of the horizon-sized volumes from part d) with a comoving volume. How many of these comoving volumes are today ( t 0 , z = 0) within one “Hubble volume” ( 4 π/ 3( c/H 0 ) 3 )? [5] Problem 2 : Steady State Model (yet again!) For the Steady State cosmological model it is assumed that the number densities of particles, photons included, remains constant as the Universe expands (and, in
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This note was uploaded on 07/28/2011 for the course PHY 880.20 taught by Professor Steigman during the Spring '10 term at Ohio State.

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probset5a - COSMOLOGY Problem Set 5 April 26, 2010 Problem...

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