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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 = , R = R , A = 4 R 2 , and V = 4 R 3 / 3. For k negationslash = 0 ( k = 1), find the leading order corrections to the following quantities for a galaxy located at comoving coordinate g ( r g ) 1. a) r g r ( g ).  b) The ratio of the proper areas A g ( k ) /A g ( k = 0), where A g A ( g ).  c) The ratio of proper volumes V g ( k ) /V g ( k = 0), where V g V ( g ).  d) If the galaxy whose comoving radial corrdinate is 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?  Problem 2 : Coasting Model Suppose we lived in an open Universe ( k < 0) in which the time-dependence 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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