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Redshift in terms of k

  1. Apr 21, 2015 #1
    Hi, I have been studying general relativity using Hobson's lately, particularly about the FRW universe.

    I know that for a matter universe with curvature,
    [tex]H^2 = \left( \frac{\dot a}{a} \right)^2 = \frac{8\pi G}{3} \rho_m -\frac{kc^2}{a^2} [/tex]
    Another expression I came across is also
    [tex]1 = \Omega_m + \Omega_k[/tex]

    I am thinking when the curvature dominates at late times what would the redshift be like.
    When curvature dominates, the FRW equation is simply ##\left( \frac{\dot a}{a} \right)^2 = \frac{8\pi G}{3} \rho_m -\frac{kc^2}{a^2} ##.

    I know that redshift is ##1+z = \frac{1}{a}##. How do I find redshift in terms of ##\Omega_k##?
  2. jcsd
  3. Apr 25, 2015 #2
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