= Uniform-density curvature perturbation
{title2=$\zeta$}
= Uniform-density curvature
{synonym}
= Constant-density curvature perturbation
{synonym}
The uniform-density curvature perturbation is the spatial scalar curvature measured on density-defined hypersurfaces, with an explicitly chosen sign convention. If the spatial scalar potentials are $C,E$, one convention is $\zeta=-C+\nabla^2E/3+\mathcal H\delta\rho/\bar\rho'$. Its two time-shift terms cancel under a <cosmological gauge transformation>. The density derivative must be nonzero. This is a different slicing from the <comoving curvature perturbation>, although the variables are related for regular adiabatic long-wavelength modes, with signs depending on convention.
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