Trying to teach myself cosmology. Given the Friedmann equation $$\left[\frac{1}{R}\frac{dR}{dt}\right]^{2}=\frac{8\pi G}{3}\rho-\frac{kc^{2}}{R^{2}}$$ and the critical density $$\rho_{c}\left(t\right)=\frac{3H^{2}\left(t\right)}{8\pi G}$$
I can see why, if $\rho>\rho_{c}$ then $k=+1.$ But I can't see why this leads to a collapsing universe? Conversely, if $\rho<\rho_{c}$ then $k=-1.$ But why does this lead to an expanding universe? I'm possibly confused because I've seen graphs of other FRW models with no correlation between the sign of $k$ and whether the universe is contracting or expanding. Do I need to learn about the deceleration parameter (I've heard of it and that's all) in order to understand this? Thank you