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I Question about an equation

  1. Jan 2, 2018 #1
    Let's suppose we have an equation,
    $$Ω_m+Ω_r+Ω_k=1$$
    In this equation whats the values that ##Ω_k## can take ?
    Only 1,0 or -1 ?

    Also this equation is true for only "now" or any time in the universe ?
     
  2. jcsd
  3. Jan 2, 2018 #2

    PeroK

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    Assuming the omegas are positive, then ##0 \le \Omega_k \le 1##

    If you allow negative values, then ##\Omega_k## can be any real number.

    That was the mathematical answer. Rereading your question, I guess you want a cosmological answer. I'll leave that to others.
     
  4. Jan 2, 2018 #3
    For flat universe we can take ##Ω_k=0##. In example for positive curvature universe then what could be the value of ##Ω_k## ?
    A negative value ?

    Cause ##Ω_k=-\frac {κ} {a^2H^2}##

    Something seems wrong to me. Either this equation only hold for ##Ω_k=0##.

    Oh okay I understand
     
  5. Jan 2, 2018 #4
    For a negative value of ##Ω_k## corresponds to ##Ω>1## which its positively curved universe
    For ##Ω_k=0## corresponds to ##Ω=1## which flat universe
    For a postive value of ##Ω_k## corresponds to ##Ω<1## which its negatively curved universe

    where ##Ω=Ω_m+Ω_r##
     
  6. Jan 2, 2018 #5

    kimbyd

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    ##\Omega_k## can be any real number that makes the equation above true. Because ##\Omega_m## and ##\Omega_r## must be positive, ##\Omega_k## cannot be greater than 1. But it can be as negative as you like.

    This is accurate.
     
  7. Jan 3, 2018 #6
    Thanks, its more clear now
     
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