  Because of the non-linearity of the Einstein equations, the cosmological
fluctuations which are generated during inflation on a wide range of
wavelengths do not evolve independently. In particular, to second order in
perturbation theory, the first order fluctuations back-react both on the
background geometry and on the perturbations themselves. I this paper, the
gravitational back-reaction of long wavelength (super-Hubble) scalar metric
fluctuations on the perturbations themselves is investigated for a large class
of inflationary models. Specifically, the equations describing the evolution of
long wavelength cosmological metric and matter perturbations in an inflationary
universe are solved to second order in both the amplitude of the perturbations
and in the slow roll expansion parameter. Assuming that the linear fluctuations
have random phases, we show that the fractional correction to the power
spectrum due to the leading infrared back-reaction terms does not change the
shape of the spectrum. The amplitude of the effect is suppressed by the product
of the inflationary slow-roll parameter and the amplitude of the linear power
spectrum. The non-gaussianity of the spectrum induced by back-reaction is
commented upon.
