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The Friedmann equation in a lambda-dominated universe

  1. Mar 20, 2007 #1
    1. The problem statement, all variables and given/known data

    Show that a lambda-dominated euclidean universe entails an exponential expansion.

    2. Relevant equations

    Equation of state is P=-E (E=epsilon)
    There is no curvature (i.e. a flat universe)

    The Friedmann equation is then

    ((a(dot)/a)^2)=((8piG)/3c^2)E + lambda/3 (eq. 1)

    which -- and this is where I get lost -- is equivalent to

    ((a(dot)/a)^2)=((8piG)/3c^2)Elambda (eq. 2)

    3. The attempt at a solution

    lambda/3 = ((8piG)/3c^2)Elambda, but if I make this substitution into the Friedmann equation, I get

    ((a(dot)/a)^2)=((8piG)/3c^2)E + ((8piG)/3c^2)Elambda

    What am I doing wrong? I'm after (eq. 2).
  2. jcsd
  3. Mar 20, 2007 #2


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    You have two different representations of the same thing in the Friedmann equation. A constant term lambda is the same thing as a vacuum energy source term satisfying rho=-p. Which one do you want to work with? You don't need both.
  4. Mar 20, 2007 #3
    I'm not sure I understand. Could you elaborate further?
  5. Mar 20, 2007 #4


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    What part don't you understand? A fluid with E=-p satisfies dE/dt=0 by the conservation equation, so is a constant. lambda is also a constant. You have two constants. It's a little redundant.
  6. Mar 23, 2007 #5
    I just wanted to say thank you for your efforts, Dick. They're appreciated. I forgot to say that. Sorry!
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