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Homework Help: Coordinate distance

  1. Jan 23, 2007 #1
    1. The problem statement, all variables and given/known data
    For a universe with [tex]k=0[/tex] and in which [tex](a/a_0) = (t/t_0)^n[/tex] where [tex]n<1[/tex], show that the coordinate distance of an object seen at redshift z is

    [tex]r=\frac{ct_0}{(1-n)a_0}[1-(1+z)^{1-1/n}][/tex].


    2. The attempt at a solution
    I have used

    [tex]r=f(r)=\int_{t}^{t_0} \frac{cdt}{a(t)}=\frac{ct_0}{(1-n)a_0}\left(t_{0}^{1-n}-t^{1-n}\right)[/tex]

    but then what? I know that [tex]1+z=\frac{a_0}{a}[/tex] but I can't get it right.
     
    Last edited: Jan 23, 2007
  2. jcsd
  3. Jan 23, 2007 #2

    HallsofIvy

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    Science Advisor

    You're missing a power of "n".
    [tex]f(r)=\int_{t}^{t_0} \frac{cdt}{a(t)}=\frac{1}{a_0}\int_{t}^{t_0}\fract_0^n t^{-n}dt= \frac{t_0^n}{a_0(1-n)}\left(t_0^{1-n}- t^{1-n}\right)[/tex]
     
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