Solution
= Solution
From the explicit solution, $\ddot a=\gamma/2$. Since $a(t_0)=1$ and $\dot a(t_0)^2=\beta+\gamma$,
$$
q_0=-\frac{\gamma}{2(\beta+\gamma)}.
$$
Because an open universe has $\beta>0$, this is strictly greater than $-1/2$. It approaches $-1/2$ only in the zero-curvature <limit>, so this model cannot attain $q_0\leq-0.5$ for the permitted parameters and therefore cannot reproduce $q_0\approx-0.55$.