hw4b-sol

# hw4b-sol - Ph 444 Solutions for Problem Set 5 1(Ryden 5.4...

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Unformatted text preview: Ph 444 Solutions for Problem Set 5 1. (Ryden 5.4) The proper distance today to a galaxy with redshift z in a flat, single- component universe with an equation of state defined by the parameter w is given by equation (5.54) from Ryden: d p ( t ) = c H parenleftbigg 2 1 + 3 w parenrightbigg bracketleftBig 1 − (1 + z )- (1+3 w ) / 2 bracketrightBig . (1) The proper distance at the time of emission of the light is d p ( t e ) = a e a d p ( t ) = d p ( t ) 1 + z . (2) If H = 70 km s- 1 Mpc- 1 , then c/H = 4300 Mpc. The proper distance for a galaxy with z = 7 in a flat radiation- ( w = 1 / 3), matter- ( w = 0), or Λ-dominated ( w = − 1) universe is given in the table below. universe d p ( t ) d p ( t e ) radiation, w = 1 / 3 c H bracketleftBig z 1+ z bracketrightBig = 3800 Mpc c H bracketleftBig z (1+ z ) 2 bracketrightBig = 470 Mpc matter, w = 0 2 c H bracketleftBig 1 − 1 √ 1+ z bracketrightBig = 5500 Mpc 2 c H (1+ z ) bracketleftBig 1 − 1 √ 1+ z bracketrightBig = 690 Mpc Λ, w = − 1 cz H = 3 . × 10 4 Mpc c H bracketleftBig z 1+ z bracketrightBig = 3800 Mpc The proper distance to a high-redshift object is strongly dependent on the cosmo- logical model. Note that some people continue to give their answers with far morelogical model....
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hw4b-sol - Ph 444 Solutions for Problem Set 5 1(Ryden 5.4...

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