(adsbygoogle = window.adsbygoogle || []).push({}); 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).

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# The Friedmann equation in a lambda-dominated universe

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