Matter density parameter = 1

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...

Ryan.

Last edited:

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