Unimodular spatial metric
= Unimodular spatial metric
{title2=$h_{ij}=a_{\mathrm{loc}}^2\gamma_{ij},\quad\det\gamma=1$}
In fixed spatial coordinates set $a_{\mathrm{loc}}=(\det h)^{1/6}$ and $\gamma_{ij}=a_{\mathrm{loc}}^{-2}h_{ij}$, so $\det\gamma=1$. This volume-shape decomposition is useful for separating isotropic expansion and anisotropic shape. The determinant-defined scale depends on the coordinate volume convention.