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Unformatted text preview: × 10-2 Mpc-3 and that in each galaxy there are 5 × 10 10 stars, and that each star has an average mass of 0 . 5M ¯ . What is the ratio ρ ? ρ c . 4. The proper distance to a source is rR where r is the comoving distance and R is the scale factor. a. Use the relation between redshift and the scale factor, i.e., 1 + z = R R ( t ) and show that 1 R ( t ) = 1 R-1 R H ( t-t ). Hint: Use Taylor series about the point t = t (the age of the Universe today) to the Frst order b. Consider the geodesic expression: cdt = R ( t ) dr √ 1-kr 2 , and assume a ²at Universe. Calculate to the Frst order the physical distance today, rR in terms of z and Hubble time t . Hint: Use the above approximation, and approximate to the Frst order....
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- Spring '10