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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 Ω

_{m}≈1

- Derive expressions for the values of

*a*at the endpoints of this range.

## Homework Equations

Ω

_{m}(

*a*) = Ω

_{m0}/[Ω

_{m0}+Ω

_{r0}/

*a*+Ω

_{v0}

*a*

^{3}].

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

## The Attempt at a Solution

Just setting Ω

_{m}=1 leads to

*a*

^{4}= -Ω

_{r0}/Ω

_{v0}, 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: