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probset5a

# probset5a - COSMOLOGY Problem Set 5 Problem 1 CDM Consider...

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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 particular, as the photons redshift).

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probset5a - COSMOLOGY Problem Set 5 Problem 1 CDM Consider...

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