= Homogeneous free scalar as a stiff fluid
{title2=$a^3\dot\phi=\mathrm{constant}$}
For a spatially homogeneous <minimally coupled scalar field> with zero <scalar potential>, the <stress-energy tensor> has $\rho=P=\dot\phi^2/2$. Its field equation is $\ddot\phi+3H\dot\phi=0$, so $a^3\dot\phi$ is constant and its <energy density> decreases as $a^{-6}$. Thus its homogeneous stress is precisely that of a <stiff fluid>. Spatial gradients would introduce directional stresses, so this equivalence requires homogeneity.
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