 Turnaround of spherical collapse

A pressureless bound spherical shell first expands, reaches $\dot{R}=0$ at its maximum radius, and recollapses. In the cycloidal spherical-collapse model, turnaround occurs at $\theta =\pi$, with $R_{\max }=2A$ and $t_{\max }=\pi B$. Its mean density is $9{\pi }^2/16$ times the background density in an Einstein-de Sitter universe.