Quantifying the behaviour of curvature perturbations near Horizon
  Crossing
  How much does the curvature perturbation change after it leaves the horizon,
and when should one evaluate the power spectrum? To answer these questions we
study single field inflation models numerically, and compare the evolution of
different curvature perturbations from horizon crossing to the end of
inflation. We find that e.g. in chaotic inflation, the amplitude of the
comoving and the curvature perturbation on uniform density hypersurfaces differ
by up to 180 \% at horizon crossing assuming the same amplitude at the end of
inflation, and that it takes approximately 3 efolds for the curvature
perturbation to be within 1 \% of its value at the end of inflation.
