Closed matter-dominated Friedmann solution

A positively curved pressureless Friedmann universe has the cycloidal parametrization $a=A(1-\cos \theta )$ and $t=B(\theta -\sin \theta )$, with $B=A/\sqrt{k}$. It expands from a Big Bang, reaches maximum size at $\theta =\pi$, and recollapses at $\theta =2\pi$.