Solution (source code)

= Solution

With $\Lambda>0$ and $k=-1$, the <Friedmann effective potential for pressureless matter> is
$$
V(a)=-\frac{\mu}{a}-\frac{\Lambda a^2}{3},
\qquad C=1.
$$
Although $V$ has one maximum, it is negative, so $C=1$ lies above it and $\dot a^2=C-V(a)$ never vanishes. An initially small expanding universe therefore expands forever. At large $a$,
$$
\frac{\dot a}{a}\longrightarrow\sqrt{\frac{\Lambda}{3}},
$$
so the expansion approaches the exponential <de Sitter scale factor in flat slicing>. \b[There is no turning point.]