Lifetime of a closed dust universe ($t_{\mathrm{BC}}=\pi {\Omega }_0/[H_0({\Omega }_0-1{)}^{3/2}]$)

The cycloidal closed matter-dominated Friedmann solution reaches its maximum scale factor at $u=\pi$ and the Big Crunch at $u=2\pi$. Thus its total lifetime is twice its time of maximum expansion. The displayed formula uses a presently expanding normalization with $H_0>0$ and $a_0=1$; the remaining time is this lifetime minus the age of a closed dust universe.