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