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Eddington-LeMaitre model (expanding universe,cosmological constant)

  1. Jan 12, 2014 #1
    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
  2. jcsd
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