# Homework Help: Friedmann's 1st equation and density parameters

1. Jan 9, 2014

### tomwilliam2

1. The problem statement, all variables and given/known data
I'm trying to work out how the expression:
$$H^2 = H_0^2 \left [ \Omega_0 \frac{a}{a_0} + 1 - \Omega_0\right]$$
can be deduced from Friedmann's first equation:
$$H^2 = \frac{8\pi G \rho}{3} - \frac{kc^2}{R^2}$$
And I have a number of questions.

Firstly, I've often seen the 1st Friedmann equation written with a $\frac{\Lambda c^2}{3}$ term in it, but my textbook gives it as above. I guess they are equivalent, but I can't see how immediately. I'd like to know how you get the first expression above from Friedmann's equation so that I can work out whether it is valid for a spatially flat universe (k=0).
I also note that there is no $\Omega(t)$ term, so the $a$ in the square brackets provides the time-dependent element. Is it possible to write the $\Omega_0\frac{a}{a_0}$ in terms of $\Omega$ instead?