Superhorizon conservation of single-field comoving curvature ($\dot{\mathcal{R}}\simeq 0(k\ll aH)$)

For an adiabatic single-field attractor, gradient terms are negligible well outside the Hubble radius and the growing comoving-curvature mode is constant. The separate-universe interpretation identifies it with the difference of local expansion histories. The conservation statement can fail for a non-attractor phase or an independent entropy mode.