Does Friedmann equation allow for complex scale factor?

[Piano man]

Looking at the Friedmann equation
$$H^2=\left[\frac{\dot{a}}{a}\right]^2=\frac{8\pi G\rho}{3}-\frac{kc^2}{a^2}$$

and considering positive curvature, then for the limit where the second term dominates, we're left with
$$\left[\frac{\dot{a}}{a}\right]^2=-\frac{kc^2}{a^2}$$

This implies a complex scale factor, does it not?

 

[Ich]

This implies a complex scale factor, does it not?

Either that, or it implies that the curvature in this limit is negative. Which is the case.
IMHO, the equation makes more sense if you rearrange it:
$$\frac{kc^2}{a^2}=\left[\frac{\dot{a}}{a}\right]^2=\frac{8\pi G\rho}{3}-H^2$$
Read: Curvature = positive contribution from energy density - negative contribution from expansion.

 

[Piano man]

Okay, so the curvature has a time dependence k=k(t)?

 

[Ich]

Right. For example, in a closed universe, it could be its radius.