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Unformatted text preview: COSMOLOGY Problem Set 1 March 31, 2010 Problem 1 : Local Universe In the limit of small distances, geometry is Euclidean (locally flat). For a flat cos mology, r = Θ, R = R , A = 4 πR 2 , and V = 4 πR 3 / 3. For k negationslash = 0 ( k = ± 1), find the leading order corrections to the following quantities for a galaxy located at comoving coordinate Θ g ≡ Θ( r g ) ≪ 1. a) r g ≡ r (Θ g ). [10] b) The ratio of the proper areas A g ( k ) /A g ( k = 0), where A g ≡ A (Θ g ). [5] c) The ratio of proper volumes V g ( k ) /V g ( k = 0), where V g ≡ V (Θ g ). [5] d) If the galaxy whose comoving radial corrdinate is Θ g has the same intrinsic lu minosity in all three cosmologies ( k = 0 , ± 1), in which cosmology will the galaxy appear to be brightest? Faintest? Why? [5] Problem 2 : Coasting Model Suppose we lived in an open Universe ( k < 0) in which the timedependence of the scale factor is: a ( t ) = ct . You may assume that the present value of the Hubble parameter in this cosmology is...
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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.
 Spring '10
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