= Shear-inclusive long-wavelength scalar equations
{title2=$3H^2=8\pi G(\Pi^2/2+V)+S^i{}_jS^j{}_i/2$}
For zero <shift vector>, negative-expansion extrinsic curvature $K=-3H$ and $S^i{}_j=\widetilde K^i{}_j$, retain the leading spatial-gradient equations of a minimally coupled scalar. They give $\dot\phi=N\Pi$, $\dot\Pi=-N(3H\Pi+V_{,\phi})$, $\dot H=-4\pi GN\Pi^2-NS^i{}_jS^j{}_i/2$, and $\dot S^i{}_j=-3NH S^i{}_j$. The first-gradient <momentum constraint> is $\partial_iH=-4\pi G\Pi\partial_i\phi-\nabla_jS^j{}_i/2$. Shear decays as $a^{-3}$ during expansion. Its neglect after inflationary damping yields the equations underlying conservation of the <nonlinear curvature covector>.
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