Critical closed radiation--cosmological-constant solution (source code)

= Critical closed radiation--cosmological-constant solution

For $\beta=4$ and $a(0)=0$, the expanding branch is
$$
a(t)=\sqrt{2(1-e^{-2H_0t})}.
$$
It grows as $2\sqrt{H_0t}$ near zero and approaches $\sqrt2$ exponentially at late times.