# First Friedmann Equation forms

dillingershaw

## Homework Statement

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

## 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.