Unimodular spatial metric ($h_{ij}=a_{\mathrm{loc}}^2{\gamma }_{ij},\det \gamma =1$)

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.