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Because of the nonlinearity 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. In this paper, the gravitational backreaction 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 backreaction 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 nongaussianity of the spectrum induced by backreaction is commented upon.
Martineau et al. (Mon,) studied this question.