Suppose I'm modelling a Universe with non-zero curvature, filled with matter, radiation and dark energy (further described by quintessence). The appropriate Friedmann equation would be of the form:
$$ H^{2}=\Big(\frac{\dot{a}}{a}\Big)^{2}=H_{0}^{2}\big(\Omega_{m,0}a^{-3}+\Omega_{r,0}a^{-4}+\Omega_{\Lambda,0}a^{-3(1+w)}+\Omega_{k,0}a^{-2}\big),$$
where $\Omega_{k}=-\frac{k}{a^{2}H^{2}}$. Now suppose I'm interested in the turning point when the Universe goes from an accelerating to a decelerating one (or vice versa) - I would achieve such a thing by setting the deceleration parameter $q=-\frac{\ddot{a}(t)a(t)}{\dot{a}^{2}(t)}$ to zero (which is in fact nothing more than setting $\ddot{a}(t)$ to zero). Taking the acceleration equation:
$$ \frac{\ddot{a}(t)}{a(t)}=-\frac{4\pi G}{3}\sum_{i}\rho_{i}\big(1+3w_{i}\big), $$
I see no way in which the curvature might manifest itself. Is this to be expected? Or did I make some sort of banal mistake in the process?