= Residual synchronous-gauge freedom
{title2=$\xi^0=C/\bar N,\quad\lambda=C\int\bar N a^{-2}dt+D$}
= Residual gauge freedom in synchronous gauge
{synonym}
Preserving $\Psi=B=0$ under the <scalar gauge transformations with a background lapse> requires $\bar N\xi^0=C(\mathbf x)$ and $\dot\lambda=C(\mathbf x)\bar N/a^2$. Thus arbitrary spatial functions $C,D$ remain after imposing <synchronous gauge in cosmology>. This freedom can generate changes in the remaining scalar metric perturbations.
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