= Conformal optical metric for scalar perturbations
{title2=$d\widehat s^2=(1+4\Psi)d\eta^2-\delta_{ij}dx^idx^j$}
Rescale the perturbed cosmological metric by $a^{-2}(1+2\phi)$. To first order, its spatial part is Euclidean and only its lapse is perturbed. The unparameterized <null geodesics> are unchanged. The nonzero linear connection coefficients are $\widehat\Gamma^0_{00}=2\partial_\eta\Psi$, $\widehat\Gamma^0_{0i}=2\partial_i\Psi$ and $\widehat\Gamma^i_{00}=2\partial^i\Psi$. The affine parameter is that of the rescaled metric, not necessarily that of the original spacetime.
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