Cosmological horizon exit

A Fourier mode exits the Hubble horizon during inflation when $k=aH$. On superhorizon scales $k\ll aH$, the growing mode of a sufficiently light scalar perturbation approaches a constant.

A cosmological mode is on a superhorizon scale when its physical wavenumber is smaller than the Hubble expansion rate, $k/a\ll H$, equivalently $k\ll aH$.