First Friedmann Equation forms

1. Sep 15, 2012

dillingershaw

1. The problem statement, all variables and given/known data
the first friedmann equation is:
($\frac{\dot{a}}{a})^2$=$\frac{8\pi G\rho}{3}$-$\frac{kc^2}{a^2}$+$\frac{\Lambda}{3}$
In the case of a closed Universe (k > 0) containing only non-relativistic matter and no cosmological constant, write the Friedmann equation in terms of, H(a), H0, a and Ω0 (where Ω0 is the current matter density parameter). Assume that the current scale factor, a0 = 1

2. Relevant equations

3. The attempt at a solution
so far what I have is:
H(a)2=H02Ω0-$\frac{kc^2}{a^2}$+$\frac{\Lambda}{3}$
I've seen things like
H(a)2=H02[$\Omega_0\frac{a}{a_0}$+1-$\Omega_0$]

but I have no explanation for this and so can't tell if it's right.

2. Sep 16, 2012

gavman

usyd student? if so try lecture 7 slide 12 ;)
I'm not sure about solving the fluid equation for p=0 - apparently its a seperable integral or something, but i think you can use what's provided on slides without proof. From there I think you are just trying to draw a relationship between the flat universe when k=0 and this closed universe for some k>0. For me, it is very time consuming to understand and show working.

I don't fully understand how we can create a single form of Friedmann for a closed universe by using flat universe equations for density, etc. Very confusing.