= Present-extrapolated spherical-collapse barrier
{title2=$\delta_c(z)/\sigma(M,0)=\delta_{\rm sc}/\sigma(M,z)$}
With linear growth normalized to unity today, a collapse threshold $\delta_{\rm sc}$ at epoch $z$ corresponds to a present-extrapolated initial barrier $\delta_c(z)=\delta_{\rm sc}/D(z)$. Comparing this barrier to present variance is equivalent to comparing $\delta_{\rm sc}$ to variance evolved to the collapse epoch. Mixing the two conventions counts growth twice.
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