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Matter density parameter = 1

  1. Oct 26, 2011 #1
    1. The problem statement, all variables and given/known data

    Starting with the equation below, I need to:
    - Show that there is a range of values for a for which Ωm≈1
    - Derive expressions for the values of a at the endpoints of this range.

    2. Relevant equations

    Ωm(a) = Ωm0/[Ωm0r0/av0a3].

    (0 signifies present day values, m=matter, r=radiation, v=vacuum)

    3. The attempt at a solution

    Just setting Ωm=1 leads to a4 = -Ωr0v0, which gives imaginary values for a, which is obviously not right. However, I can't see any other way of solving this problem to get real values...


    Thanks in advance,
    Ryan.
     
    Last edited: Oct 26, 2011
  2. jcsd
  3. Oct 26, 2011 #2

    George Jones

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    The question is unclear to me. What does [itex]\Omega_m \approx 1[/itex] mean? Clearly, the expression gives [itex]\Omega_m \left( a \right) < 1[/itex] always. To get a handle on things, I had my computer plot [itex]\Omega_m \left( a \right)[/itex]. Try finding the values of [itex]a[/itex] for which [itex]\Omega_m \left( a \right) > 0.95[/itex]. Instead of 0.95 you could use some other number nearer to or farther from 1.
     
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