The Friedmann equation in a lambda-dominated universe

[_Andreas]

Homework Statement

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

Homework 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)

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).

 

[Dick]

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.

 

[_Andreas]

I'm not sure I understand. Could you elaborate further?

 

[Dick]

I'm not sure I understand. Could you elaborate further?

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.

 

[_Andreas]

I just wanted to say thank you for your efforts, Dick. They're appreciated. I forgot to say that. Sorry!