Eddington-LeMaitre model (expanding universe,cosmological constant)

1. Jan 12, 2014

shooride

I'm trying to solve Friedmann equations for $k=1$ & $p=0$ (matter).
These are equations:
$$3(\dot{R}^2 +1)/R^2 -λ =8πGε$$
$$(2R\ddot{R}+\dot{R}^2 +1)/R^2 -λ=0$$
If we use $(\dot{R}^2 +1) /R^2$ and put it in the second equation:

$\ddot{R}+ω^2/6=0$ & $ω^2=8πGε-2λ$

If $ω^2=0$, then we have Einstein's static model.
Furthermore, for $ω^2>>0$, the solution is like $R=A\exp(ωt)$ or $R=A\sin(ωt)+B\cos(ωt)$with suitable constants. But I know Eddington-LeMaitre model (expanding universe) and the solution above, it's not that and it doesn't have coasting period or others property of that model. I don't know that what is the my wrong?!!!
Can anyone help me?
Thanks for your consideration on my problem.

Last edited: Jan 12, 2014