I don't know GR so while answering the question so keep in mind that.
In the Friedmann Equations, is energy density has an effect on curvature or vice versa? Or they are separate things and they don't affect each other?
For example can we have an energy density $\rho_0$ such that its less then a critical density $\rho_c\,,\,\,(\rho_0<\rho_c)$ in a positive curvature universe ?
Or a hyperbolic universe with $\rho_0>\rho_c$. In general, it seems it should affect, but I couldn't be sure.