## Abstract

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.

Original language | English |
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Article number | 044013 |

Journal | Physical Review D |

Volume | 63 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2001 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)