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Relationship betwen ##Ω_k## and ##k##

  1. May 19, 2015 #1
    ##H^2(t)-8ρπG/3=-k/a^2(t)## (Lets suppose a(t)=1) then
    ##H^2(t)-8ρπG/3=-k## In equations ##k## can be -1,0,1.
    Then If ##k<0## then ##-k>0## then
    ##H^2(t)-8ρπG/3>0 ##→Hyperbolic Universe. This means ##Ω_k>0## I mean If ##k## negative ##Ω_k## must be positive isnt it ? I am confused here.
    In cosmology calculator says ##Ω_k=1-Ω_m-Ω_Λ##

    (Its look like hyperbolic universe I am trying to understand)

    ThanksΩ
     
  2. jcsd
  3. May 19, 2015 #2

    Chalnoth

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    Science Advisor

    Yes, ##\Omega_k## has a sign opposite to ##k##. Specifically, ##\Omega_k = -k/H_0^2## (note: this assumes the we're using the convention where ##a(now) = 1##. For the convention where ##k = {-1, 0, 1}##, ##\Omega_k = -k/H_0^2a^2(now)##).
     
  4. May 19, 2015 #3
    Thanks
     
  5. May 19, 2015 #4
    I made a mistake soory
     
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