Back reaction problem in the inflationary universe

We investigate the back reaction of cosmological perturbations on an inflationary universe using the renormalization-group method. The second-order zero mode solution which appears by the nonlinearity of the Einstein equation is regarded as a secular term of a perturbative expansion; we redefine the constants of integration contained in the background solution, and the secular terms are absorbed in these constants in a gauge-invariant manner. The resulting renormalization-group equation describes the back reaction effect of inhomogeneity on the background universe. For a scalar-type classical perturbation, by solving the renormalization-group equation, we find that the back reaction of the long wavelength fluctuation works as a positive spatial curvature, and the short wavelength fluctuation works as a radiation fluid. For the long wavelength quantum fluctuation, the effect of back reaction is equivalent to a negative spatial curvature.