# The Friedmann equation in a lambda-dominated universe

## 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
Homework Helper
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.

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

Dick