= Dimensionless spherical-collapse time normalization
{title2=$\tau\sim(8/9\pi)y^{3/2}$}
For <spherical collapse> in an <Einstein-de Sitter universe>, take $y=R/R_{\rm ta}$ and $\tau=H_{\rm ta}t$, with $\Delta_{\rm ta}=(3\pi/4)^2$. The expanding branch has $\tau=\Delta_{\rm ta}^{-1/2}\int_0^y[u/(1-u)]^{1/2}\,du$. Its small-radius expansion is $\tau=(8/9\pi)y^{3/2}(1+3y/10+O(y^2))$, and its turnaround time is $2/3$. These constants are linked: using another leading coefficient without changing the time normalization no longer gives a <density contrast> approaching zero at early times. The collapsing branch is $4/3-\tau_{\rm expand}(y)$.
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