We investigated the back reaction of cosmological perturbations on the
evolution of the universe using the second order perturbation of the Einstein's
equation. To incorporate the back reaction effect due to the inhomogeneity into
the framework of the cosmological perturbation, we used the renormalization
group method. The second order zero mode solution which appears by the
non-linearities of the Einstein's equation is regarded as a secular term of the
perturbative expansion, we renormalized a constant of integration contained in
the background solution and absorbed the secular term to this constant. For a
dust dominated universe, using the second order gauge invariant quantity, we
derived the renormalization group equation which determines the effective
dynamics of the Friedman-Robertson-Walker universe with the back reaction
effect in a gauge invariant manner. We obtained the solution of the
renormalization group equation and found that perturbations of the scalar mode
and the long wavelength tensor mode works as positive spatial curvature, and
the short wavelength tensor mode as radiation fluid.Comment: 18 pages, revtex, to appear in Phys. Rev.
