= Uniform-density curvature sign test
{title2=$\zeta=-\Phi+\delta\rho/[3(\bar\rho+\bar P)]$}
For spatial metric $a^2(1-2\Phi)\delta_{ij}$, the combination $\zeta=-\Phi+\delta\rho/[3(\bar\rho+\bar P)]$ is invariant under a time displacement: $\Phi$ shifts by $\bar NH T$ and $\delta\rho$ by $3\bar NH(\bar\rho+\bar P)T$. The opposite overall sign is also valid. The sum $\Phi+\delta\rho/[3(\bar\rho+\bar P)]$ is not invariant. This is a useful convention check before applying <superhorizon conservation of uniform-density curvature>.
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