= Scalar-field stress projections
{title2=$\rho,\mathcal J_i,S_{ij}$}
For a <minimally coupled scalar field>, put $q^2=h^{ij}D_i\phi D_j\phi$ using the <spatial covariant derivative>. Spatial and normal projections of its <stress-energy tensor> give $\rho=\Pi^2/2+q^2/2+V$, $\mathcal J_i=-\Pi D_i\phi$, and $S_{ij}=D_i\phi D_j\phi+h_{ij}(\Pi^2/2-q^2/2-V)$. The trace-free stress is $D_i\phi D_j\phi-h_{ij}q^2/3$, with coefficient one. This makes the scalar <anisotropic stress> second order in a spatial gradient expansion.
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