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Unformatted text preview: 11 Geometry of Universe •  An isotropic/homogeneous Universe can have an ____, ______ or _____ geometry •  Angles of a triangle sum to ____ than 180°, _____ than 180°, or 180° in these geometries •  A closed Universe is ______ in extent •  Latest data indicate that we live in a _____ Universe; un8l this was known the other two op8ons of more interest. 5/21/13 UW, ASTR 323, SP13, Eric Agol ©2013 12 Use geometry to deduce the curvature of the Universe: ds=D r=d dθ _ Flat + us ds2 = D 2 = Sκ (r )2 dθ 2 ! # dθ = D / Sκ (r ) = " # $ UW, ASTR 323, SP13, Eric Agol ©2013 5/21/13 13 Robertson- Walker Metric •  For homogeneous, isotropic Universe metric is: 2 2 2% "2 2 2 2 d = −(cdt ) + a(t ) $(dr ) + Sκ (r ) # ( r sin(r / r ) c κ = +1 *c * Sκ (r ) = ) r κ =0 * r sinh(r / r ) κ = −1 c *c + {(dθ ) + (sinθdφ ) }'& •  κ<0, κ=0, κ>0 for an open, flat & closed Universe 5/21/13 UW, ASTR 323, SP13, Eric Agol ©2013 14 Newtonian cosmolo...
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