Renormalization group approach to cosmological back reaction problems

We investigate the back reaction of cosmological perturbations on the evolution of the Universe using the second order perturbation of Einstein's equation. To incorporate the back reaction effect due to inhomogeneity into the framework of the cosmological perturbation, we use the renormalization-group method. The second-order zero mode solution which appears by the nonlinearities of 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 in this constant. For a dust-dominated universe, using the second-order gauge invariant quantity, we derive the renormalization-group equation which determines the effective dynamics of the Friedmann-Robertson-Walker universe with the back reaction effect in a gauge-invariant manner. We obtain the solution of the renormalization-group equation and find that perturbations of the scalar mode and the long wavelength tensor mode work as a positive spatial curvature, and the short wavelength tensor mode as a radiation fluid.