= Scalar expansion perturbation
{title2=$\kappa=\delta K$}
With negative <extrinsic curvature> convention, the background <trace> is $\bar K=-3H$. The scalar expansion perturbation is $\kappa=K+3H$. For <lapse function> $N=\bar N(1+\Psi)$, <induced metric> $h_{ij}=a^2[(1-2\Phi)\delta_{ij}+2E_{,ij}]$ and <shift vector> $N_i=-a^2B_{,i}$, it is $\kappa=3(\dot\Phi/\bar N+H\Psi)-\Delta\chi$, where $\chi$ is the <scalar shear potential>. The expansion of the future normal congruence is $-K$, so its perturbation has the opposite sign.
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