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Matter density parameter = 1

  • Thread starter ryanwilk
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  • #1
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Homework Statement



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.

Homework Equations



Ωm(a) = Ωm0/[Ωm0r0/av0a3].

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

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:

Answers and Replies

  • #2
George Jones
Staff Emeritus
Science Advisor
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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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