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 secular terms of a perturbative expansion, we redefine constants of integration contained in the background solution and absorbed the secular terms to these constants in a gauge-invariant manner. The resulting renormalization-group equation describes the back reaction effect of inhomogeneity on the background universe. For 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. PACS number(s): 04.25.Nx, 98.80.Hw Typeset using REVTEX e-mail: [email protected] 1