Lifetime of a closed dust universe
= Lifetime of a closed dust universe
{title2=$t_{\rm BC}=\pi\Omega_0/[H_0(\Omega_0-1)^{3/2}]$}
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>.