 Solution

Inflation produces the primordial comoving curvature perturbation while modes exit the Hubble radius. Its adiabatic super-Hubble conservation allows that initial amplitude to be carried through the end of inflation and subsequent changes of the background equation of state without solving each mode's full evolution at every intervening time. After Hubble re-entry, cosmological transfer functions relate it to the cosmic microwave background temperature and polarization fluctuations and to the matter power spectrum. The conserved curvature perturbation connects inflationary initial conditions to later cosmological observables. This bridge uses the adiabatic conditions stated in part (v); entropy perturbations can supply an additional evolving source.